Discrete Probability Distributions/Probability Distributions Question 01 What is a random variable?  Give an example of a discrete random variable and a continuous random variable.  Justify your answer.

]]> A random variable represents a numerical value assigned to an outcome of a probability experiment.  Examples will vary.

]]> 3.0000000 0.0000000 0 editor 15 0 ]]> Question 02 What is a discrete probability distribution?  What are the two conditions that determine a probability distribution?

]]> A discrete probability distribution lists each possible value a random variable can assume, together with its probabilty.

Condition 1:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«mo»§#8804;«/mo»«mi»P«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»§#8804;«/mo»«mn»1«/mn»«/math»

Condition 2:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mo»§#8721;«/mo»«mrow/»«/msub»«mi»P«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mn»1«/mn»«/math»

]]> 3.0000000 0.0000000 0 editor 15 0 ]]> Question 03 The expected value of an accountant's profit and loss analysis is 0.  Explains what this means.

]]> An expected value of 0 represents the break-even point, so the accountant will not gain or lose any money.

]]> 1.0000000 0.0000000 0 editor 15 0 ]]> Question 04 What is the significance of the mean of a probability distribution?

]]> The mean of a probability distribution represents the "theoretical average" of a probability experiment.

]]> 1.0000000 0.0000000 0 editor 15 0 ]]> Question 05 In most applications, continuous random variables represent counted data, while discrete random variables represent measured data.

]]> 1.0000000 1.0000000 0 True False In most applications, discrete random variables represent counted data, whereas continuous random variables represent measured data.

]]> ]]> Question 06 For a random variable «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» the word random indicates that the value of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» is determined by chance.

]]> 1.0000000 1.0000000 0 True False ]]> Question 07 The mean of a random variable represents the "theorectical average" of a probability experiment and somtimes is not a possible outcome.

]]> 1.0000000 1.0000000 0 True False ]]> Question 08 The expected value of a descrete random variable is equal to the standard deviation of the random variable.

]]> 1.0000000 1.0000000 0 True False The expected value of a dicrete random variable is equal to the mean of the random variable.

]]> ]]> Question 13-20 Decide whether the random variable x is discrete or continuous.

  1. x represents the number of motorcycle accidents in one year in California.
    {#1}

  2. x represents the length of time it takes to get work.
    {#2}

  3. x reprersents the volume of blood drawn for a blood test.
    {#3}

  4. x represents the number of rainy days in the month of July in Orlando, Florida.
    {#4}

  5. x represents the number of home theater systems sold per month at an electronics store.
    {#5}

  6. x represents the tension at which a randomly selected guitar's strings have been strung.
    {#6}

  7. x represents the amount of snow (in inches) that fell in Nome, Alaska last winter.
    {#7}

  8. x represents the total number of die rolls required for an individual to roll a five.
    {#8}
]]> 8.0000000 0.3333333 0 ]]> Question 23 Dependent Children

A socioligist surveyed the households in a small town.  The random variable x represents the number of dependent children in the households.  Determine the probability distribution's missing probability value.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math»
 #a #b #c «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»?«/mo»«/math» #d
]]> 1.0000000 0.3333333 0 0 #sol <session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>12</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>17</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>23</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>35</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>41</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>10</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mn>1</mn><mo>-</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mn>1</mn><mo>-</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.14884</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>#solinlineEditorand]]> Question 24 Dependent Children

A sociologist surveyed the households in a neighboring town.  The random variable x represents the number of dependent children in the household.  Determine the probability distribution's missing probability.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»6«/mn»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math» #a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»?«/mo»«/math» #b #c #d #e #f
]]> 1.0000000 0.3333333 0 0 #sol <session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>05</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>20</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>26</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>18</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>24</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>14</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>10</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>08</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mn>1</mn><mo>-</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>+</mo><mi>e</mi><mo>+</mo><mi>f</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.085049</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>#solinlineEditorand]]> Question 25 Tires

A mechanic check the tire pressures on each car that he worked on for one week.  The random variable x represents the number of tires that were underinflated.  Decide whether the distribution is a probability distribution.  If it is not a probability distribution, identify the property (or properties) that are not satisfied.

x 0 1 2 3 4
P(x) 0.30 0.25 0.25 0.15 0.05
]]> 1.0000000 0.3333333 0 false true abc Yes, the distribution is a probability distribution.

]]> No, the distribution is not a probability distribution.

]]> The sumation of the random variable probabilities is not equal to 1.

]]> One of the random variable probabilities is less than 0 or greater than 1.

]]> ]]> Question 26 Phone Lines

A company recorded the number of phone lines in use per hour during one work day.  The random variable x represents the number of phone lines in use.  Decide whether the distribution is a probability distribution.  If it is not a probability distribution, identify the property (or properties) that are not satisfied.

 

x 0 1 2 3 4 5 6
P(x) 0.135 0.186 0.226 0.254 0.103 0.64 0.032
]]> 1.0000000 0.3333333 0 false true abc Yes, the distribution is a probability distribution.

]]> No, the distribution is not a probability distribution.

]]> The summation of the probability of the random variables is not equal to 1.

]]> The probability of one random variable is less than or greater than 1.

]]> ]]> Question 27 Quality Control

A quality inspector cheched for imperfection in rolls of fabric for one week. The random variable x represents the number of imperfections found. Decide whether the distribution is a probability distribution. If it is not a probability distribution, identify the property (or properties) that are not satisfied.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»10«/mn»«/mfrac»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»20«/mn»«/mfrac»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»25«/mn»«/mfrac»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»50«/mn»«/mfrac»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»100«/mn»«/mfrac»«/math»

 

 

 

]]> 1.0000000 0.3333333 0 false true abc Yes, the distribution represents a probability distribution.

]]> No, the distribution does not represnt a probability distribution.

]]> The summation of the probabilities of the random variables is not equal to 1

]]> One of the probabilities of the random variables is less than 0 or greater than 1

]]> ]]> Question 28 Golf Putts

A golf tournament director recorded the number of putts needed on a hole for the four rounds of the tournament.  The random variable x represents the number of putts needed on the hole.  Decide whether the distribution is a probability distribution.  If it is not a probability distribution, identify the property (or properties) that are not satisfied.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«mo».«/mo»«mn»007«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«mo».«/mo»«mn»292«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«mo».«/mo»«mn»349«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«mo».«/mo»«mn»245«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«mo».«/mo»«mn»058«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«mo».«/mo»«mn»004«/mn»«/math»
]]> 1.0000000 0.3333333 0 true true abc Yes, the distribution is a probability distribution.

]]> No, the distribution is not a probability distribution

]]> The summation of the probabilities of the random variable is not equal to 1.

]]> One of the probabilities of the random variable is less than or greater than 1.

]]> ]]> Question 29 Dogs

Use the frequency distribution to construct a probability distribution.

The number of dogs per household in a small town.

Dogs «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«/math»
Households #a #b #c #d #e #f
  1.  
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math»
    0 {#1}
    1 {#2}
    2 {#3}
    3 {#4}
    4 {#5}
    5 {#6}
  2. Find the probability of randomly selecting a household that has fewer than two dogs.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mrow»«mi»x«/mi»«mo»§lt;«/mo»«mn»2«/mn»«/mrow»«/mfenced»«mo»§#160;«/mo»«mo»=«/mo»«/math» {#7}

  3. Find the probability of randomly selecting a household that has at least one dog.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mrow»«mi»x«/mi»«mo»§#8805;«/mo»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#160;«/mo»«mo»=«/mo»«/math» {#8}

  4. Find the probability of randomly selecting a household that has between one and three dogs, inclusive.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mrow»«mn»1«/mn»«mo»§#8804;«/mo»«mi»x«/mi»«mo»§#8804;«/mo»«mn»3«/mn»«/mrow»«/mfenced»«mo»§#160;«/mo»«mo»=«/mo»«/math» {#9}

  5. Find the mean to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#956;«/mi»«mo»=«/mo»«/math» {#10}

  6. Find the variance to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»§#963;«/mi»«mn»2«/mn»«/msup»«mo»=«/mo»«/math» {#11}
  7. Find the standard deviation to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#963;«/mi»«mo»=«/mo»«/math» {#12}

 

]]> 12.0000000 0.3333333 0 <session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1400</mn><mo>.</mo><mo>.</mo><mn>1500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>400</mn><mo>.</mo><mo>.</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>200</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>50</mn><mo>.</mo><mo>.</mo><mn>75</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>+</mo><mi>e</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mfrac><mrow><mi>b</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mfrac><mrow><mi>c</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mfrac><mrow><mi>e</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mrow><mi>f</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sola</mi><mo>=</mo><mi>h</mi><mo>+</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solb</mi><mo>=</mo><mn>1</mn><mo>-</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solc</mi><mo>=</mo><mi>i</mi><mo>+</mo><mi>j</mi><mo>+</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi><mo>=</mo><mn>0</mn><mo>*</mo><mi>h</mi><mo>+</mo><mn>1</mn><mo>*</mo><mi>i</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>j</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>l</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi><mo>=</mo><mi>h</mi><mo>*</mo><msup><mfenced><mrow><mn>0</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>i</mi><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>j</mi><mo>*</mo><msup><mfenced><mrow><mn>2</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>k</mi><mo>*</mo><msup><mfenced><mrow><mn>3</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>l</mi><mo>*</mo><msup><mfenced><mrow><mn>4</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>m</mi><mo>*</mo><msup><mfenced><mrow><mn>5</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi><mo>=</mo><msqrt><mi>var</mi></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1436</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>483</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>176</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2203</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.546</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.831</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.911</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sola</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.871</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solb</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.348</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solc</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.333</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.652</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.219</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.0799</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.0336</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.0109</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.00454</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]> Question 30 Cats

Use the frequency distribution to construct a probability distribution.

The number of cats per household in a small town.

Cats «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«/math»
Households #a #b #c #d #e #f

 

  1. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math»
    0 {#1}
    1 {#2}
    2 {#3}
    3 {#4}
    4 {#5}
    5 {#6}
  2. Find the mean to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#956;«/mi»«mo»=«/mo»«/math» {#7}

  3. Find the variance to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»§#963;«/mi»«mn»2«/mn»«/msup»«mo»=«/mo»«/math» {#8}

  4. Find the standard deviation to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#963;«/mi»«mo»=«/mo»«/math» {#9}

 

]]> 9.0000000 0.3333333 0 <session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1800</mn><mo>.</mo><mo>.</mo><mn>2000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>300</mn><mo>.</mo><mo>.</mo><mn>400</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>190</mn><mo>.</mo><mo>.</mo><mn>210</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>70</mn><mo>.</mo><mo>.</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>50</mn><mo>.</mo><mo>.</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>35</mn><mo>.</mo><mo>.</mo><mn>45</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>+</mo><mi>e</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mfrac><mrow><mi>b</mi><mo>+</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mfrac><mrow><mi>c</mi><mo>+</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mo>+</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mfrac><mrow><mi>e</mi><mo>+</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mrow><mi>f</mi><mo>+</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi><mo>=</mo><mn>0</mn><mo>*</mo><mi>h</mi><mo>+</mo><mn>1</mn><mo>*</mo><mi>i</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>j</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>l</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi><mo>=</mo><mi>h</mi><mo>*</mo><msup><mfenced><mrow><mn>0</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>i</mi><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>j</mi><mo>*</mo><msup><mfenced><mrow><mn>2</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>k</mi><mo>*</mo><msup><mfenced><mrow><mn>3</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>l</mi><mo>*</mo><msup><mfenced><mrow><mn>4</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>m</mi><mo>*</mo><msup><mfenced><mrow><mn>5</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi><mo>=</mo><msqrt><mi>var</mi></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.52289</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3.6127</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.9007</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]> Question 31 Computers

Use the frequency distribution to construct a probability distribution.

The number of computers per household in a small town.

Computers
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«/math»
Households #a #b #c #d

 

  1. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math»
    0 {#1}
    1 {#2}
    2 {#3}
    3 {#4}
  2. Find the mean to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#956;«/mi»«mo»=«/mo»«/math» {#5}

  3. Find the variance to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»§#963;«/mi»«mn»2«/mn»«/msup»«mo»=«/mo»«/math» {#6}

  4. Find the standard deviation to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#963;«/mi»«mo»=«/mo»«/math» {#7}

 

]]> 7.0000000 0.3333333 0 <session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>90</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>110</mn><mo>.</mo><mo>.</mo><mn>120</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>80</mn><mo>.</mo><mo>.</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>60</mn><mo>.</mo><mo>.</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mfrac><mrow><mi>b</mi><mo>+</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mfrac><mrow><mi>c</mi><mo>+</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mo>+</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi><mo>=</mo><mn>0</mn><mo>*</mo><mi>h</mi><mo>+</mo><mn>1</mn><mo>*</mo><mi>i</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>j</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi><mo>=</mo><mi>h</mi><mo>*</mo><msup><mfenced><mrow><mn>0</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>i</mi><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>j</mi><mo>*</mo><msup><mfenced><mrow><mn>2</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>k</mi><mo>*</mo><msup><mfenced><mrow><mn>3</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi><mo>=</mo><msqrt><mi>var</mi></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.3011</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7.0714</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.6592</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]> Question 32 DVDs

Use the frequency distribution to construct a probability distribution.

The number of defects per batch of DVDs inspected.

Defects
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«/math»
Batches #a #b #c #d #e #f

 

  1. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math»
    0 {#1}
    1 {#2}
    2 {#3}
    3 {#4}
    4 {#5}
    5 {#6}
  2. Find the mean to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#956;«/mi»«mo»=«/mo»«/math» {#7}

  3. Find the variance to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»§#963;«/mi»«mn»2«/mn»«/msup»«mo»=«/mo»«/math» {#8}

  4. Find the standard deviation to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#963;«/mi»«mo»=«/mo»«/math» {#9}

 

]]> 9.0000000 0.3333333 0 <session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>90</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>110</mn><mo>.</mo><mo>.</mo><mn>120</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>80</mn><mo>.</mo><mo>.</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>60</mn><mo>.</mo><mo>.</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>+</mo><mi>e</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mfrac><mrow><mi>b</mi><mo>+</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mfrac><mrow><mi>c</mi><mo>+</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mo>+</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mfrac><mrow><mi>e</mi><mo>+</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mrow><mi>f</mi><mo>+</mo><mn>0</mn></mrow><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi><mo>=</mo><mn>0</mn><mo>*</mo><mi>h</mi><mo>+</mo><mn>1</mn><mo>*</mo><mi>i</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>j</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>l</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi><mo>=</mo><mi>h</mi><mo>*</mo><msup><mfenced><mrow><mn>0</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>i</mi><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>j</mi><mo>*</mo><msup><mfenced><mrow><mn>2</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>k</mi><mo>*</mo><msup><mfenced><mrow><mn>3</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>l</mi><mo>*</mo><msup><mfenced><mrow><mn>4</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>m</mi><mo>*</mo><msup><mfenced><mrow><mn>5</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi><mo>=</mo><msqrt><mi>var</mi></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.60585</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4.8157</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.1945</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]> Question 33 Overtime Hours

Use the frequency distribution to construct a probability distribution.

The number of overtime hours worked in one week per employee.

Overtime hours
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»6«/mn»«/math»
Employees #a #b #c #d #e #f #g

 

  1. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math»
    0 {#1}
    1 {#2}
    2 {#3}
    3 {#4}
    4 {#5}
    5 {#6}
    6 {#7}
  2. Find the mean to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#956;«/mi»«mo»=«/mo»«/math» {#8}

  3. Find the variance to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»§#963;«/mi»«mn»2«/mn»«/msup»«mo»=«/mo»«/math» {#9}

  4. Find the standard deviation to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#963;«/mi»«mo»=«/mo»«/math» {#10}

 

]]> 10.0000000 0.3333333 0 <session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>4</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>14</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>25</mn><mo>.</mo><mo>.</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>50</mn><mo>.</mo><mo>.</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>40</mn><mo>.</mo><mo>.</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>25</mn><mo>.</mo><mo>.</mo><mn>35</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mn>14</mn><mo>.</mo><mo>.</mo><mn>18</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>+</mo><mi>e</mi><mo>+</mo><mi>f</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>h</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mfrac><mrow><mi>b</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>h</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfrac><mrow><mi>c</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>h</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>h</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mrow><mi>e</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>h</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mfrac><mrow><mi>f</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>h</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mfrac><mrow><mi>g</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>h</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi><mo>=</mo><mn>0</mn><mo>*</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>*</mo><mi>j</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>l</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>m</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>6</mn><mo>*</mo><mi>o</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi><mo>=</mo><mi>i</mi><mo>*</mo><msup><mfenced><mrow><mn>0</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>j</mi><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>k</mi><mo>*</mo><msup><mfenced><mrow><mn>2</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>l</mi><mo>*</mo><msup><mfenced><mrow><mn>3</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>m</mi><mo>*</mo><msup><mfenced><mrow><mn>4</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>n</mi><mo>*</mo><msup><mfenced><mrow><mn>5</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>o</mi><mo>*</mo><msup><mfenced><mrow><mn>6</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi><mo>=</mo><msqrt><mi>var</mi></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.4584</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40.686</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6.3786</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]> Question 34 Extracurricular Activities

Use the frequency distribution to construct a probability distribution.

The number of school-related extracurricular activities per student.

Activities
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»6«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»7«/mn»«/math»
Students #a #b #c #d #e #f #g #h

 

  1. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math»
    0 {#1}
    1 {#2}
    2 {#3}
    3 {#4}
    4 {#5}
    5 {#6}
    6 {#7}
    7 {#8}
  2. Find the mean to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#956;«/mi»«mo»=«/mo»«/math» {#9}

  3. Find the variance to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»§#963;«/mi»«mn»2«/mn»«/msup»«mo»=«/mo»«/math» {#10}

  4. Find the standard deviation to 3 significant digits.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#963;«/mi»«mo»=«/mo»«/math» {#11}

 

]]> 11.0000000 0.3333333 0 <session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>17</mn><mo>.</mo><mo>.</mo><mn>22</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>37</mn><mo>.</mo><mo>.</mo><mn>42</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>50</mn><mo>.</mo><mo>.</mo><mn>55</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>55</mn><mo>.</mo><mo>.</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>66</mn><mo>.</mo><mo>.</mo><mn>71</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>39</mn><mo>.</mo><mo>.</mo><mn>44</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mn>25</mn><mo>.</mo><mo>.</mo><mn>30</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mn>15</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>+</mo><mi>e</mi><mo>+</mo><mi>f</mi><mo>+</mo><mi>g</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>i</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfrac><mrow><mi>b</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>i</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mfrac><mrow><mi>c</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>i</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>i</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mfrac><mrow><mi>e</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>i</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mfrac><mrow><mi>f</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>i</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mrow><mi>g</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>i</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mfrac><mrow><mi>h</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn></mrow><mi>i</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi><mo>=</mo><mn>0</mn><mo>*</mo><mi>j</mi><mo>+</mo><mn>1</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>l</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>m</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>o</mi><mo>+</mo><mn>6</mn><mo>*</mo><mi>p</mi><mo>+</mo><mn>7</mn><mo>*</mo><mi>q</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi><mo>=</mo><mi>j</mi><mo>*</mo><msup><mfenced><mrow><mn>0</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>k</mi><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>l</mi><mo>*</mo><msup><mfenced><mrow><mn>2</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>m</mi><mo>*</mo><msup><mfenced><mrow><mn>3</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>n</mi><mo>*</mo><msup><mfenced><mrow><mn>4</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>o</mi><mo>*</mo><msup><mfenced><mrow><mn>5</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>p</mi><mo>*</mo><msup><mfenced><mrow><mn>6</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>q</mi><mo>*</mo><msup><mfenced><mrow><mn>7</mn><mo>-</mo><mi>me</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi><mo>=</mo><msqrt><mi>var</mi></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3.4136</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>303.46</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17.42</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]> Question 35 Quiz

Students in a class take a quiz with eight questions.  The number x of questions answered correctly can be approximated by the following probability distribution. 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»6«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»7«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»8«/mn»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math» #a #b #c #d #e #f #g #h #i
  1. Find the mean of the probability distribution to three significant digits.
    {#1}

  2. Find the variance of the probability distribution to three significant digits.
    {#2}

  3. Find the standard deviation of the probability distribution to three significant digits.
    {#3}

  4. Find the expected value of the probability distribution to three significant digits.
    {#4}
]]> 4.0000000 0.3333333 0 <session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>02</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>02</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>06</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>06</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>08</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>22</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>16</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>08</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>30</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi><mo>=</mo><mn>0</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>*</mo><mi>b</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>c</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>d</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>e</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>f</mi><mo>+</mo><mn>6</mn><mo>*</mo><mi>g</mi><mo>+</mo><mn>7</mn><mo>*</mo><mi>h</mi><mo>+</mo><mn>8</mn><mo>*</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mn>0</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mo>(</mo><mn>1</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mo>(</mo><mn>2</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>d</mi><mo>*</mo><mo>(</mo><mn>3</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>e</mi><mo>*</mo><mo>(</mo><mn>4</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>f</mi><mo>*</mo><mo>(</mo><mn>5</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>g</mi><mo>*</mo><mo>(</mo><mn>6</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>h</mi><mo>*</mo><mo>(</mo><mn>7</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>i</mi><mo>*</mo><mo>(</mo><mn>8</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi><mo>=</mo><msqrt><mi>var</mi></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.02</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.02</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.06</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.06</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.08</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.22</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.08</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5.3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3.25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.8028</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]> Question 36 911 Calls

A 911 service center recorded the number of calls received per hour.  The number of calls per hour for one week can be approximated by the following probability distribution.  

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»6«/mn»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»7«/mn»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math» #a #b #c #d #e #f #g #h

 

  1. Find the mean of the probability distribution to three significant digits.
    {#1}

  2. Find the variance of the probability distribution to three significant digits.
    {#2}

  3. Find the standard deviation of the probability distribution to three significant digits
    {#3}

  4. Find the expected value of the probability distribution to three significant digits.
    {#4}
]]> 4.0000000 0.3333333 0 <session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>01</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>10</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>26</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>33</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>18</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>06</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>03</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>03</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi><mo>=</mo><mn>0</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>*</mo><mi>b</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>c</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>d</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>e</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>f</mi><mo>+</mo><mn>6</mn><mo>*</mo><mi>g</mi><mo>+</mo><mn>7</mn><mo>*</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mn>0</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mo>(</mo><mn>1</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mo>(</mo><mn>2</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>d</mi><mo>*</mo><mo>(</mo><mn>3</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>e</mi><mo>*</mo><mo>(</mo><mn>4</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>f</mi><mo>*</mo><mo>(</mo><mn>5</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>g</mi><mo>*</mo><mo>(</mo><mn>6</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>h</mi><mo>*</mo><mo>(</mo><mn>7</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi><mo>=</mo><msqrt><mi>var</mi></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3.02</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.92</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.39</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]> Question 37 Hurricanes

The histogram shows the distribution of hurricanes that have hit the U.S. mainland by category, with 1 the weakest level and 5 the strongest.

  1. Find the mean of the probability distribution to three significant digits.
    {#1}

  2. Find the variance of the probability distribution to three significant digits.
    {#2}

  3. Find the standard deviation of the probability distribution to three significant digits.
    {#3}

  4. Find the expected value of the probability distribution to three significant digits
    {#4}
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The histogram shows the distribution of occupants in cars crossing the Tocoma Narrows Bridge in Washington each week.

  1. Find the mean of the probability distribution to three significant digits.
    {#1}

  2. Find the variance of the probability distribution to three significant digits.
    {#2}

  3. Find the standard deviation of the probability distribution to three significant digits.
    {#3}

  4. Find the expected value of the probability distribution to three significant digits.
    {#4}
]]> 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lSyRs1vbTgxkzLDIxBzhiFVl5I+wvjX/AME/PhL8aP2g/E3xM/4Tj4yfC/xL4o0xdN8X/wDCDeJFsYPEFuI0i8u6jkikDKY40UqMIwUFlJyTp/EL9gT4DeOfgF8JfAWlf8Jn8Ml+GjO3gzXfBusfY9T08ysrzHznRw7SSIsjOV378srLlslLSnBVNdY37u3Nd3vs7x93TRW9bqJc0uTS/NZ9rpWVtr3v72+t/JfL+qeN/wBtvxH+3P4N/Y40v4+eCvBvjfQvA914o8XfEu08HW13LrcZvpYbSNLKZRFG3kvaGRYwuHMuHZVAfyK+/bb/AGpF/wCCXOmarbeIfCUPxu8P/tCRfDfVdd/siN9P1yJIXkLyJ5WxBI+1XaBVYIuVCFhX2TrX/BNj4Naho/gS40b4ifHrwZ478MWV1Zp470Lxh5Ou6pFdXFxczi7nMTK5eW6uGLIiE+YQSVwK7CP9gH4DWn7HfgH4J6S/jLRPDHhbxpbeL1vrS/g/tDVtThVl828leBlcOrAMERMBEC7AuK1hy3959Vf/AMGKV12XJeNut9gbScml0dvL3Gkn/wBvtPrbufCd946/4KMWXx8/aK+CP/DR3gKbUPhv4Sj8ZP4wk8EWaXV7E1oJksIIViMUcTPvVnkjZ18sEHDba3te/a9+J3j/APZB/Zl1LS/2kYfgz8RfF/hG51DU9G8MfCd/Futa5cW9xJbGVLZFeO2tmaCVs5ViwbapVGC/pRd/s2+Bbz9ov4w/E2XVPFY174keEIvDGuW63UItre1jiaIPbr5O5ZSGOS7Ouf4R0r52n/4JtfByHw98Krfwz8Rvjx4E1fwJoFxoNlr3hvxTFZajqGnz3M1y9vcyJbhSN9xMAYljJD4bdhdvPDndO0t9Pw9ovy9ndbXu7XHPl57x7P0/5dv8/aW7aLRHc/8ABP8A+Ofjb9oX/gmZ4S+IHxGuba/8arf3mnapewWaWy3bQTFVlMaYRWKFN21VXcDhQMCvxj+G3ibxb+zL/wAFD/il+14Lq4vfg9ffHzxJ8P8A4iWNvbO72VtJOtzFdHbneA8hcYUENbhAT52K/fn9nP8AZ78F/sx/szWXwq8Bal4m1bw/bX9xeJc69cwzXTPM25gWiiiTA4Awg981w+n/ALG/whtf2afjl8KL9vE3iDwn8VfFN/4k8Qrqd1C81re3hjYtaskKiMRPFG8e8OysoJZuldFdx9pKcF9m3q24cy9GlJeVzGlC8OSps5fcves/VPlfyPy5+BXxe1b4c/8ABBv4C2Phb4+WHwL1jxP451y3tr238CSeKdX1NFvp28mxsFVgzFmjDO+0KHUBgzKDnQftzftUp/wT71yTTfHNlq3xS0D9oS08FW3iDW/BsGmvqunzQ3Dxx3dkyYtnaSEBwqJKinbu3gtX6CTf8E5Pgyn7MPwk+GuieN/jL4Wufhtq99qfhTxdo/iCC21u2lvJPMnUypbiPaWCYKxKw8tcNy+6DSP+CbXwS0n4V3nhNvGvxl1a3u/iTaePbrUNS1y1uL2fUbZJVVZJWtcvE3nOz7gZGY58z1IqHNaT0937k4X/AAUuyd9jWdSTlz2V3zv5y9pb5XcH1a+SPAPip4w/bq8CftGfsufs16R+0B4Q1D4lePdO1w6/4vuvCVmtsBFILhJ0hEHEkFukiIoAWRj845DK3WfiT+2h8W/2rPjr8Lvhh8efCvwsh+BfhHT11fUZPClnfTeLtWlsvNklkE0ZW2haSKcZjXailP3bk/L+i3jH9n/wZ43/AG1/hN8eNW1LxNB4v+HtrfW+i2lpcwrYzreQtFKZ0aJnYhWJXZImD1z0rwb41/8ABPz4S/Gj9oPxN8TP+E4+Mnwv8S+KNMXTfF//AAg3iRbGDxBbiNIvLuo5IpAymONFKjCMFBZSck5NP2cV1fNfyd3yP0Seq6uzd+VWaUFO/T3fnqudfO2j6apWuz4d8F/8FD/izpus/s5/Fz4t63o2k/Bzx78NfEEOoaZDp0MMA8Q6PNdD7QkzR+bm4WO0jWISFN87KFyAa4z4Uft5ftKfEj9nD4W/CuXxomlftNeI/jPZ6TeXE3h6xivY/DU9ql0br7G8HlqgEmBL5XMa7gSTur9Kfir+wF+z/wDFb9jL4b/Am6tPE3g3wR4Hu/tOgv4bvIY7xGZJFlEkk8MwcStIZJDt3M4DZHfb039iT4J6T/wUbsf2nrCLxLb+PLPSI9OttOW8i/suPy7IWCTiLyvMEot1CZ83bxnbnmuhTj7aUmvdvp6KXP8AK/wdbR/HGcX7JKOjs7+rXKvuXvf4td7W+LP2XP2lf2gfFH/BU3UPh3+0X8Xb34c+JJdW1GGw+Dmq/DSK1tNRs0hlME9hq64kcq0ZYeYCsqIxV33Db2n/AAUpsr7Ufjz+xnZab8MNJ+NF9N431BYfBGp3sFrba2fssf7iSWcGJB3y4I+WvfPh1+wZ8NfAH7WPhr4v3/xJ+O3xN1zwwlynhLTfHHi7+07DQVnUqwtkMSuAEYqoZ2HIJDMFYekftGfst+Dv2lY/AUniXxn8TvAeqeD9Rmv9E1XwPrEWn3sMsqKjHzXhlIwFGCm0jnmuWtDmpUUt4uN/SMk+t7tpa3ur6baLoU17Wq+klK3k3Fq2nRN6bO3nqfin8K/iR8RP2Yf2bP8Agoz/AGHod58CPjTpOt6NrWn+DEtrXUdK8OWl3fJGot5CZIpm8q7Ccps2LCy7uQn0v8StY/aH8O+C/wBirxD8dvGHw5+JXijxt8d9GvLPb4LsHj8P2F3FC32G2aSAsjIxJFwpEuQvz/Lk/XNn/wAE6fgJafsy/FX4cPq3xP1O++I32MeLvGmp+IVvPEF8LW4S5iHnSxNEvzp82IfmB5ztUr7X8R/2ZvAXxP0n4G2Wv6p4ts4fhV4isNc8O/2fdQIbmeyVViS53wtvjIUbgnlsezCuqnJc0HPVp0vS0Wua1/JLfV69zKfvKVtL+0fZ3kla9tN+Z6aK6Pxx/aG+Jn7Vf7Q37HP7a3j+0+KPhTwv8CfBPi+fwi3w+bQIHuL22trqAPP9qZDLHMd0DYLEMWlA8vauYfih+2N8Yvh5p3gr4b+DPjxZfBweGvgl4YvvCmg2XgGLxDdeNtSudPgY2ksrpJ9jIyFUkKCCDhiQa+//AB9/wTA+AXxA+KfxK8Q3Xi/40eHdK8c6g+qa54X0PxNHBpDagzF/tggaB90gdpHUSF1VpGwoXCj4x+MH7Gf7QXhj9tn4qa38MPhX8SfG2gX/AIN0bRPh74o8H/Fyz8MXGmNY6fBZq+oI+x7hwYFkIAWM7RjlyY+SinGCg768rfduMJp6vvKV430X4LSaUqjl/it0+KcGtOlopptav7mdB8RP2m/2stL+KXwY+AV58UfFHgzxyPhZb+LvHHirw58H08RavdX1y7lbJtMjTbBFCpjjeVUQ71JIGQlfWnwQ8eftr/F/9kP9nvxXc2PhrwF4ntPGEtt8V7TxdoE+mXWraVDMFEtpA0R8uWSHJOAimTBUqmVEdh+whceP/g18FfE/xf8Ai58W/C/7S/hXwmmi6x8QPh94sey1C9g3yOLaWd43M2zzSplwryHJZmBAr2W7/Y58Cap4K+A2ka54++MPiK4+FHio+JNH1fVvEi3V/qt4ZjMft8rxHzkLHGFCELlQQCQe1uKrS2tz302tz3uvLl05dE1p5nLDmdODW/L13vyWs/Pm1vq1vfofW9FFFc5sFFFFABRRRQAUUUUAFFFFABXwQepr73r4IPU0AfXXww/5Idon/bb/ANHyV3tcF8MP+SHaJ/22/wDR8ld7QAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAVWvLy007SLrUL+5gsrG1haa5uJ3CRxRqCzOzHgKACST0AqzXz/APtW6Fr/AIn/AOCZ3x78PeFrS61DxDqHgPVLextLaPfLcO1rIPKQZGWblR7kcHpWOIqOnSlNdE2aUYKdSMX1aPm7wz/wU2/Z68Y/GnT/AA14d8P/ABj1LwtfeIYNAtfiAnhJh4da+nZFiiMxk81CzSIAHhB+YEgL81fofvTzvL3r5mM7c849cV+UH7DP7Xf7K3hv/glh8EfA95468M+FvFlp9n0K78KyRl9Rm1SW62eatvGrPIk0sgl84AqvmfOylWx+V3iT4gfDzxB8fvhn8d/hT4S0b4f+Nbn46wxvq2o/Fm61XxjqkJncyNdaaAsVtaMGRNwwQMRBpFYse10f9oVFa62v84peXW+j2tvuczq/uZVrWS6dtJO1/wDt19N0/Q/qwLKHVSyhm+6CeTXzt+0R+1J8KP2ZPB2g6h8RLzWr3WdfumtfDvhvQLH7ZqusTLt3JBDuUHBdBudlXc6LnLAH88f2MPgb4Q8f/wDBVz9rD4z+KL7xJqHifwB8a9Xh8K2v9pOLKye4M8c8pi6M7xiOM56CJP7ox037Xfijw18Kf+Dgf9j34r/FQppfwti0DU9Mj127jY2mn37LcKruRkLg3FvlmACg784QleWLbdFN257fK8eZfN/CvNr0OmpDklWS15Lr1alyv5Lf0TPq/wCAv7bvwj+Pnxv1j4XafovxI+G3xR020N5N4S8eaAdNv3gXYWkQK8icCRG2MwcqdwUqCR9hb0MpQMpcDJXPIFfjH4u+InhH49f8HIfwd8S/s93Gj/EOT4cfDvV5/E3iXRZPPs2aW0u0tbfzl+SXbJcxgFSRm4Zc5Rgvzj+yVc/Aq7/ZiHx2T4ma7qv/AAUIuo/Fc1vYvrlxNqGq3y6dqDQ289mQym38lI5hIQg85ETzMgRG3Ney57WtFyfylKKsvNRu9dL9boFRvVUFK92lfom4qTu+lumnrazP6Kgyl2UMpZfvAHkU6v51v2d9B/ZOn/4JoeIvHuj/ABH1HXP2vvFXwq8ZReIrCXX7i51DVJWsruSdLm1JcBVSNZI5DsMhG7c54EmlfGv4a+OvC/8AwSU8CeEfGGn6v4x8NeJdPi8Q6VbOTNprRm2tiswHCFmR9oJyy/NjBBrX2T9vGitW5QWm3vScbrukle+l/K1zB1F7B1ulpvXR+7GLSfZy5rW6W67H9EZdVZQzKpY4UE9aGdFdVZ1VmOFBOCfpX8mnjGD4JT/sq/tT+MvEnxL16x/aX8K/Ge6Pw30ZfEE8b2cEmpRySz2tuCBudvtLySqSUaCI5Qkb/Yv2xPFXw88f/Ff45TeIPBWjW3xj8G+FtFafxV43+KtzpmoR3zWNsTFomjRqEmYMrM6tuG5y5KblFcyqXpKduibS7OKlo9m1ezvazt3OiVO03G/Vpeqly69r7rfZ9j+mpmCoWYhVAySTwKAylNwYFSM5zxivwKf4faV+1L/wUq/Y78JfFvVvFOpaD4h/ZX07U/ENtY6zNbNqsoMspWdw291aVY5W5yzxISTivBYPF+t2H/BDT4bfDzxP4z8Uaf8ABdP2l5fCPizUI7t/Nh8PIgla2d0GfK+aaTaBjKAAYwtdFSlKNSVP7Sbt2aVVUr36atP0uYt2ipW6K/len7S3nomj+m5WV0DIyup6EHINOr8DPjD4H+APwR+CHw7/AGmv2OPFeoeLfCHwV+L6TeJbLTdafUrO2tNRtrCO9tbWeXPmI6rbgkSOFe8ny4I2p9m/8E3dLv8Axd8KfjN+1Dr0FzDrXxm8eXeqWS3J/eQ6VayyQWcJ7fITOoxxtC80QgpKT/lWunX3WvvUm7/3X01CpeCj/e2/8mv91l/4Ej9JqKKKzGFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFfBB6mvvevgg9TQB9dfDD/AJIdon/bb/0fJXe1wXww/wCSHaJ/22/9HyV3tABRRRQAUVwdn8T/AABqHxovfh5Z+KdLuPGdoHFxpiMd6ukcUrxhsbDKkc8MjRhi6pLGzKFYE0dR+MHw00rUfE9tqHi7Trc+HSqa1KVkMFpKzRKtu0oUobhmngAgDGUmWMBPmXJ/w/y7js72+R6VRXkVv8e/g7dX/h+1g+IGgyXOsyrFZRb2DLI109kkcwK/6O7XUclsqzbC06NEAXUqPWZpobe3aaeWOCJfvPIwVR9SafK7X/rTcT3sSUVm/wBs6P8A9BbTf/ApP8ar3XiTw7Y6bPeXuvaLZ2cEZkmnnvY0jjUDJZmJwABySaTYG1RXKv468EReE49fk8Y+FY9CkRXj1FtWhFsysQFYSbtpBJGDnnNRD4g+Am1HTbNfG/hBrvUYhLp8A1iDfdoQSHiXfl1IBIK5HBoDpc6+iuY0vxt4M12GeXRPF3hjWI4JPLmex1WGYRvjO1irHBx2Nav9taP/ANBbTf8AwKT/ABoA0qKzf7a0f/oLab/4FJ/jR/bWj/8AQW03/wACk/xoA87t/gR8EbT4xf8ACw7X4PfC638ffaTc/wDCSReFrNdRExBBl+0CPzPMIJBfdk561ny/s5fs9z+OLrxNP8C/g9P4juNRXUp9Uk8G2LXMl2rFxcmQxbjNuZm8zO7JJzk16p/bWj/9BbTf/ApP8aP7a0f/AKC2m/8AgUn+NC0tbpsD1vfqZfh/wX4O8J6lr974V8J+GfDN5rl+2oa3PpWlw2smpXTfeuLho1BllOTl3yx9aTxf4J8GfEHwXN4b8eeEvDXjXw9K6vJpmu6ZDfWzsvKsY5VZdw7HGR2rV/trR/8AoLab/wCBSf40f21o/wD0FtN/8Ck/xpNJqzHd3ucx4F+GPw3+F+h3emfDbwB4L+H+nXUwmurbw7osFhHPIBgO6wooZscZOTjis/Svg18ItC+Ml78RdE+Fvw80fx/dtI114ksvDtrDqUxk/wBYWuFQSEt/ES3zd812/wDbWj/9BbTf/ApP8aP7a0f/AKC2m/8AgUn+NU22+bqLpbocJ4c+Cvwd8HfEfVPGPhL4UfDfwx4t1JZV1DWtJ8N2lreXQlYPKJJo4w7B2AZgT8xGTk1maH+z18A/DOp2V74c+CXwk0K8s9SXU7OfT/CNlBJbXajC3EbLECkoHAdcEdjXp39taP8A9BbTf/ApP8aP7a0f/oLab/4FJ/jQna3l/wAP+eoPVNPr/wAMfGfwG/YZ+F3wm1TxvrXjTRPh/wDFrxZrHxCvfFmka9qvgu2W80UTmJo7eKWRpX/dvGXDqy/M2Qqnk/Qvi/4C/A34geOH8TePPg38LPGviNoBA+qa94Us765aNRhUMksbMVAJABPGeK9H/trR/wDoLab/AOBSf40f21o//QW03/wKT/Gi/uxj0SSXolb8lbz6ju+Zy6vX8b/mc3p3w0+HGj+LtD8QaT4A8E6Xr2i6Mui6PqVpodvFc6fp6/ds4JVQNFbjJxEpCD0qknwi+FEXws1nwNF8Mfh7D4K1e5e61Xw/H4dtV0++mcqXlmtxH5ckjFVJZlJJUHPArsf7a0f/AKC2m/8AgUn+NH9taP8A9BbTf/ApP8aUvevfr/nf89fUS0/ryt+WnofOPxj/AGZPD3jX/gnl43/Z++E3/CJfAzR/EaJHJNonhaBraFDNHJP/AKLG0Kl5EQoX3AjdnqBXs3wx8A6P8K/2dvBHw28P7m0bwzoltpdrIyhWlWGNU8xgP4mILH3Y11H9taP/ANBbTf8AwKT/ABo/trR/+gtpv/gUn+NNNrm87X+V7fdd/eJq9vK9vna/5I0qKzf7a0f/AKC2m/8AgUn+NH9taP8A9BbTf/ApP8aQzSorN/trR/8AoLab/wCBSf40f21o/wD0FtN/8Ck/xoA0qKzf7a0f/oLab/4FJ/jR/bWj/wDQW03/AMCk/wAaANKis3+2tH/6C2m/+BSf40f21o//AEFtN/8AApP8aANKis3+2tH/AOgtpv8A4FJ/jR/bWj/9BbTf/ApP8aANKis3+2tH/wCgtpv/AIFJ/jR/bWj/APQW03/wKT/GgDSorN/trR/+gtpv/gUn+NSQ6nptxcrDb6hYzzN91I51ZjxngA0AXq+CD1Nfe9fBB6mgD66+GH/JDtE/7bf+j5K72uC+GH/JDtE/7bf+j5K72gAooooA+RpfhT8XbT9oKTWNNtPh1eeGNA8T6v4t8LT3PiC8hvdRv76wltRY3sQtJFgt0a6uW8+OSVtqQgQjDV5XL+y38X7D4k+L9R0HxLo50f8A4S248VaZY6l421eey8QXb+I7PXLeG5sHia30oQeRPbC4tBM0vn+c8eQ0bfobRVU5un7Pl0cEkvRWt91l+ty+d+8v5nzPzevf1fo3payt8Caf+zd8XIfF2t3V1N8Nls/Hmq6dqfjNodWvGl0BrLxFe60sNgDbAXwdLzyPMkNqUdDNsff5K/eN7Y2WpaZLZajZ2t/Zy48yC5iWSN8EEZVgQeQD+FWqKlWSSXTT5JWS9EtEKcpSk5N6t3fq938zx34d+DPB918MEmuvCnhu5m/tTUF3y6ZCzbVvrhVGSvQAAD0AArlvjr8JdK8Rfs+PbeF/ht4c8R6pY+ING1Z9GgtLO3k1S3stUtbu4tUeYLFvkihkRVkdEZiFd0Viw8Qb9sTwX8LtZ1nwJq3hfxRqGoaXrF6Jbi08nyn8y5lmGNzg8CQDkdQaX/h4H8Ov+hK8a/8Akv8A/HK++wXhhxViaNPE0MHJxkoyi/d1Ts09X6b/ADPDqcS5bSqOE6qTTae/oyCP4OXP/DKOvaDqvwD8XWF9eeKp/FWmW3hL/hF31HTDca1cXcFmov5jZtLCgikmRt8GJikbzFTWbYfBv4j2vxL+EurS/Da4k8aPpGl2njjV/wCyvC58MzWVvPdvLBNFxex6iIbhwHsY47Zp3iJJhRkGz/w8D+HX/QleNf8AyX/+OUf8PA/h1/0JXjX/AMl//jldEPCTi+KUVgZWVtLx6K2vva6JXvvZXuZz4qyqUpS9sru/fq79u+q6K7tY7H9mr4SX3hnQPEej+JvhveaB4Es4rC08I6b430vw9LrkAihZLjzJtILwSW2BbiJpWa4LLOZGKtHj6e/4QTwR/wBCb4V/8FMH/wATXxh/w8D+HX/QleNf/Jf/AOOVZsv2+fh3e6zaWY8G+NIzPMsQYi3O3cQM/wCt96qt4U8Xv3pYGX3rot/i36vzEuKMrb/jrX1/yPsb/hBPBH/Qm+Ff/BTB/wDE0f8ACCeCP+hN8K/+CmD/AOJrfs7yK9s/OiOQHZD7EEgj8xVuvzc985X/AIQTwR/0JvhX/wAFMH/xNH/CCeCP+hN8K/8Agpg/+JrqqKAOV/4QTwR/0JvhX/wUwf8AxNH/AAgngj/oTfCv/gpg/wDia6qigDlf+EE8Ef8AQm+Ff/BTB/8AE0f8IJ4I/wChN8K/+CmD/wCJrqqKAOV/4QTwR/0JvhX/AMFMH/xNH/CCeCP+hN8K/wDgpg/+JrqqKAOV/wCEE8Ef9Cb4V/8ABTB/8TR/wgngj/oTfCv/AIKYP/ia6qigDlf+EE8Ef9Cb4V/8FMH/AMTR/wAIJ4I/6E3wr/4KYP8A4muqooA5X/hBPBH/AEJvhX/wUwf/ABNH/CCeCP8AoTfCv/gpg/8Aia6qigDlf+EE8Ef9Cb4V/wDBTB/8TR/wgngj/oTfCv8A4KYP/ia6qigDlf8AhBPBH/Qm+Ff/AAUwf/E0f8IJ4I/6E3wr/wCCmD/4muqooA5X/hBPBH/Qm+Ff/BTB/wDE0f8ACCeCP+hN8K/+CmD/AOJrqqKAOV/4QTwR/wBCb4V/8FMH/wATR/wgngj/AKE3wr/4KYP/AImuqooA5X/hBPBH/Qm+Ff8AwUwf/E0f8IJ4I/6E3wr/AOCmD/4muqooA5X/AIQTwR/0JvhX/wAFMH/xNH/CCeCP+hN8K/8Agpg/+JrqqKAOV/4QTwR/0JvhX/wUwf8AxNWrHwn4V0zVIr7TfDXh/T72PPl3Ftp0UciZBBwyqCMgkfQmugooAK+CD1Nfe9fBB6mgD66+GH/JDtE/7bf+j5K72uC+GH/JDtE/7bf+j5K72gAooooAKK+C4fjEmjft06hBrPxYEN5pnifWU8ceE7/VIUtPDvhq30zzrTUWgZVaGMzC0b7USQ7XsqF3VUEXBeLPjRq+hfE74oeF4PibY61BFrsdxrvi3wz43/tFPBmknxLY213a6jZm3EekTpZXUypLvclLS6lYx+TuNU4ufs7fbV126b9rX16Kz30vTjbmv9mXL+evntp1d18v0xor8qNH+Mfi2fx7HZR/GLX7s/21pifCK1N7Gx8a2Mni3ULW8kX93/xM4102O1Uygv5cBW63KZBOf1J1OC/udEnh0y/TTL5gPKuXtxMI+QT8hIzkZHXvmla8VLv/AF96vqt09GE48s3Ht/Wnl2ez3Wh+A/xy/wCTu/iF/wBhmX+deU16f8aUmj/ar8dx3M4ubhdVkEsoj2B24y23Jxk9s15hX+lXAv8AyTeX/wDXml/6RE/njOv+RhX/AMcvzYUUUV9SeYFauh/8jto//X9F/wChisqtXQ/+R20f/r+i/wDQxWWI/hS9GXD4kf0SeF/+QBP/ANfs/wD6MaujrybQdG8by2N9Ja+N7K1tm1C4McLaCjlF81sDd5gzj1xW5/YXj7/of7H/AMJ1P/jtf5Yy3P6VR3tFcF/YXj7/AKH+x/8ACdT/AOO0f2F4+/6H+x/8J1P/AI7SA72iuC/sLx9/0P8AY/8AhOp/8do/sLx9/wBD/Y/+E6n/AMdoA72iuC/sLx9/0P8AY/8AhOp/8do/sLx9/wBD/Y/+E6n/AMdoA72iuC/sLx9/0P8AY/8AhOp/8do/sLx9/wBD/Y/+E6n/AMdoA72iuC/sLx9/0P8AY/8AhOp/8do/sLx9/wBD/Y/+E6n/AMdoA72iuC/sLx9/0P8AY/8AhOp/8do/sLx9/wBD/Y/+E6n/AMdoA72iuC/sLx9/0P8AY/8AhOp/8do/sLx9/wBD/Y/+E6n/AMdoA72iuC/sLx9/0P8AY/8AhOp/8do/sLx9/wBD/Y/+E6n/AMdoA72iuC/sLx9/0P8AY/8AhOp/8do/sLx9/wBD/Y/+E6n/AMdoA72iuC/sLx9/0P8AY/8AhOp/8do/sLx9/wBD/Y/+E6n/AMdoA72iuC/sLx9/0P8AY/8AhOp/8do/sLx9/wBD/Y/+E6n/AMdoA72iuC/sLx9/0P8AY/8AhOp/8do/sLx9/wBD/Y/+E6n/AMdoA72iuC/sLx9/0P8AY/8AhOp/8do/sLx9/wBD/Y/+E6n/AMdoA72iuC/sLx9/0P8AY/8AhOp/8dq/pek+L7bXIJ9U8X2mqWK7vNtU0VYDJlSB84kOMHB6c4x3oA66vgg9TX3vXwQepoA+uvhh/wAkO0T/ALbf+j5K72uC+GH/ACQ7RP8Att/6PkrvaACiiigAwM5xz60mBzwOevvS0UAJgccDjp7UtFFAH8/Pxy/5O7+IX/YZl/nXlNerfHL/AJO7+IX/AGGZf515TX+lfAv/ACTeX/8AXml/6RE/nrOv+RhX/wAcvzYUUUV9SeYFauh/8jto/wD1/Rf+hisqtXQ/+R20f/r+i/8AQxWWI/hS9GXD4kf0SeF/+QBP/wBfs/8A6MaujrnPC/8AyAJ/+v2f/wBGNXR1/li9z+lUFFFFIAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAK+CD1Nfe9fBB6mgD66+GH/JDtE/7bf+j5K72uC+GH/JDtE/7bf+j5K72gAor5G+NP7XnhX4EftO+Fvh74v8K63rcPiK3ibTJvCt7bapqqysZt3m6Oji+MAEORPDHKpO5SFKjd9OeGPEmk+MPh5o3inQpLuXR9UtEurRrqymtJtjDI3wzKskbdijqrA8EA0LWPMthyTjKz3tf5Hk+nfG+C+/aKtvBknhTUbXQL/X77w9pHiM3sLx3upWVqbq4i8hSXSMLHcosjcmS2kBVQY2k5fxT+07oegfGXxX4MsPB/iTX7nSRYWtpfwvFDaanqV5qNtp4s4XdhkQy3dv50oBVMyqNzxOg3rv8AZ902f4wa14vt/iJ8SNNa5uLy/wBI0q3msHs/D+pXdsLWfUbPzLR5ROY/Mws0ksKmeYiL5uMTX/2TPhLq/j2/8VaXF4i8GeI57VkgvdA1HyhaXJ1SHVvtscUivEbj7ZAkp3o8bEuHRg7A1TspUXPa3v23vbpfTfb5N9UEvt27rl/w3W/ny7+d7dDBs/2rba6168sH+HWvQtoGo2mn+NpP7St2XRpbrWrnRoTFzm6Tz7SWZiBGRblG2lz5Q+qtTvhpuiT3xtL6/EQH7izh82V8kD5V79c/QGvm2z/ZU8IWniDTtQ/4Tf4k3Be5gu/FNvNeWZi8W3Fvqc+qwzXwFqChS7uZpNtobZGVhEytEqxj6gpfZV9+vr1+V72623bY58vO+Xbp6dL+ffpfY/ny+NM32n9qvx3ceVNB5uqyP5cybXTODhh2I7ivMK9W+OX/ACd38Qv+wzL/ADrymv8ASrgX/km8v/680v8A0iJ/PGdf8jCv/jl+bCiiivqTzArV0P8A5HbR/wDr+i/9DFZVauh/8jto/wD1/Rf+hissR/Cl6MuHxI/e7QfGq2tjfW58K+Nbjy9QuF8yDSWdHxKwypzyPetz/hPU/wChP8e/+CZv8a2vC/8AyAJ/+v2f/wBGNXR1/li9z+lUcF/wnqf9Cf49/wDBM3+NH/Cep/0J/j3/AMEzf413tFIDgv8AhPU/6E/x7/4Jm/xo/wCE9T/oT/Hv/gmb/Gu9ooA4L/hPU/6E/wAe/wDgmb/Gj/hPU/6E/wAe/wDgmb/Gu9ooA4L/AIT1P+hP8e/+CZv8aP8AhPU/6E/x7/4Jm/xrvaKAOC/4T1P+hP8AHv8A4Jm/xo/4T1P+hP8AHv8A4Jm/xrvaKAOC/wCE9T/oT/Hv/gmb/Gj/AIT1P+hP8e/+CZv8a72igDgv+E9T/oT/AB7/AOCZv8aP+E9T/oT/AB7/AOCZv8a72igDgv8AhPU/6E/x7/4Jm/xo/wCE9T/oT/Hv/gmb/Gu9ooA4L/hPU/6E/wAe/wDgmb/Gj/hPU/6E/wAe/wDgmb/Gu9ooA4L/AIT1P+hP8e/+CZv8aP8AhPU/6E/x7/4Jm/xrvaKAOC/4T1P+hP8AHv8A4Jm/xo/4T1P+hP8AHv8A4Jm/xrvaKAOC/wCE9T/oT/Hv/gmb/Gj/AIT1P+hP8e/+CZv8a72igDgv+E9T/oT/AB7/AOCZv8aP+E9T/oT/AB7/AOCZv8a72igDgv8AhPU/6E/x7/4Jm/xq/pfi5dT1yCxHhvxdYGXd+/vdMMUKYUn5mzxnGB7kV11FABXwQepr73r4IPU0AfXXww/5Idon/bb/ANHyV3tcF8MP+SHaJ/22/wDR8ld7QB+MHxH8SX+qf8FGPHOu2/7R/wAItHsdavrLRNS8MWf7QGj6XdwRaff3KLalG0Wa4QyKySPEk0cqySyxGVwsZT9n6/Gz41fEz4AaH+3Ff6HoPiL/AISo6JeWl14hki/aW1DSbhru+1e6WaysdNhd4rq4tnDNJA7xeXG0MeFQKR+ydOn/ALvDvrr939fPqZyusRPXotPv/S33BRWXHrmiy+Lrjw/FrGly69BbrcT6al2huY4mOFkaPO4ITwGIwarf8JR4aNxrUI8RaEZdHXfq6fb492nrtLZnG790NoJy2OBmpujQ3aK5+PxZ4WlfQ1i8S+H5G1pS2jBdRiJ1EAbiYPm/egDn5M8c10FOwXP5+fjl/wAnd/EL/sMy/wA68pr1b45f8nd/EL/sMy/zrymv9K+Bf+Sby/8A680v/SIn89Z1/wAjCv8A45fmwooor6k8wK1dD/5HbR/+v6L/ANDFZVauh/8AI7aP/wBf0X/oYrLEfwpejLh8SP6JPC//ACAJ/wDr9n/9GNR4q8W+HPBHg6XX/FOq2+j6Uk8VuJZAzNJNNIsUMMaKC0kskjqiRoCzMwABJxR4X/5AE/8A1+z/APoxq434ueGfFviHwZ4evfA0Ph6+8VeH/EdprFlYa7qE1lZXwj3RywyTwxStGTFLIVfypAHVCVPUf5XzbUl6q/pdXfyV2f0tFXT9HbzdtF5Xel+m5qX3xV+Hun/BvTfiDP4osZPB2oIr2Wp2yPcJOGVmyqxqzHCo7Nx8oRi2ApxQg+NfwnufG1v4et/H/hmfU57YXEOy7BhkU2v20KJv9UZDa/6T5e7f5P73bs+avCbn4bftD6L+xxcfDjwRJ8NLTW9Vv3u9X1WTxReWr2y6lqF7e6vDZyDT5djxieOG1uHQk72keNDGqSczdfs2eN734g6HLoGj+A/hZ4c0iyN/b2Nj4rvNdsJdUHhuTQ4Ijp09jbxJbQpKqmQSHzY7SPMCNM5S5Rs6ivtt9zevS21rX1utNG7pRjLl5na61+9W/W/bR66o+vPB3j7wh4/0m+vfCGt2+sQ2VyLe8VY3ikgkaNJkDxyKrKGikjkUkYdHVlJVgT2FfM/7Mvwh8U/CD4feKtN8Smwg/tPUre5tbOHxPc+IJYBFYW1q3mahdW1vNMGMGUjdCIkCohCBY4/pinNRT93b+v6797Mxg21dhRRRUFBRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFfBB6mvvevgg9TQB9dfDD/kh2if9tv/AEfJXe1wXww/5Idon/bb/wBHyV3tAH5Sftd+I/Fehft4aBpvhb4l6n4Xski0J7jRdJsJEsbNLu8v4pr7U7mPSLpYlaVLRUElxCJFW4w0ZUOf1br8cf2lfhu3h3/gobLHo9l8TdRi1+HRLs2l1feM9XTxlK2rXLy6clzZ3gstPhslxMkdzG8SG5yEC5z+x1VCV6Kvvd/p/XfyWxM42ry7Wj+p8PL4G+IOjfteXPiOy+EOq3o0HxdrfipvFNnqOko3iu3u9L+ywaXHvuI50nDtboftKRwBdOiPmt8mOH+I/wAJvif4u/aj8X+LNJ+FviO68LWP2J20jXLjw/bprH2TxFpepPDpRtZtzx3UdndSyf2sUbzmgVXiR5wP0ZoopycHSlHemrJ/LlTfnb5dy5WfPdfE7v1vzadtde66WPzH0v4D/E2Px3rFxL8IWs4fGuuaXqmn3Z1PTCPAkdp4u1DW5Y7lVm3ea8N3E6/YvtCm4DIzqirM36VanpljrGiT6bqUAubKYASxFiu7BDDkEHqBV6iktIqPb8tl+C33fVtjnNzm5Pd6/wBf5bLZWR/Pl8abeG0/ar8d2tunl28OrSJGmSdqjAA5rzCvVvjl/wAnd/EL/sMy/wA68pr/AEq4F/5JvL/+vNL/ANIifzxnX/Iwr/45fmwooor6k8wK2PDwDeP9DU8g6hCD/wB/FrHrZ8Of8lB0L/sIwf8AoxawxP8ABn6P8i6Xxo+oviL+0L448P8A7RHxA0XTdN8Gx2Nl4lv4IQ+iozbUuZFBJzyeOTXHf8NPfEb/AJ8PBX/gjT/GvOvjB/ydp8Uf+xu1L/0rlrzqvgso8PeGamBoTlgKbbjFt8i3svI9zFZ9mMa00q8t31fc+iv+GnviN/z4eCv/AARp/jR/w098Rv8Anw8Ff+CNP8a+daK9D/iHPC//AEL6X/gC/wAjn/t/Mv8An/L72fRX/DT3xG/58PBX/gjT/Gu/+Ffx58Z+Mv2jfBnhXWtP8JNpOqarFbXYg0hI5DGxwQrA5U+45r42r1/4Af8AJ6nwy/7D9v8A+hV5Of8Ah/w1SyzE1IYGmpKEmnyLRqLs9jqwOe5hLE04yrSabXV9z9q9F8AeBdV8MWd+fDsaGaMNt+0zcf8Aj9av/CsPAv8A0AI//Amb/wCLrW8Gf8k00n/riK6ev89T93OC/wCFYeBf+gBH/wCBM3/xdH/CsPAv/QAj/wDAmb/4uu9ooA4L/hWHgX/oAR/+BM3/AMXR/wAKw8C/9ACP/wACZv8A4uu9ooA4L/hWHgX/AKAEf/gTN/8AF0f8Kw8C/wDQAj/8CZv/AIuu9ooA4L/hWHgX/oAR/wDgTN/8XR/wrDwL/wBACP8A8CZv/i672igDgv8AhWHgX/oAR/8AgTN/8XR/wrDwL/0AI/8AwJm/+LrvaKAOC/4Vh4F/6AEf/gTN/wDF0f8ACsPAv/QAj/8AAmb/AOLrvaKAOC/4Vh4F/wCgBH/4Ezf/ABdH/CsPAv8A0AI//Amb/wCLrvaKAOC/4Vh4F/6AEf8A4Ezf/F0f8Kw8C/8AQAj/APAmb/4uu9ooA4L/AIVh4F/6AEf/AIEzf/F0f8Kw8C/9ACP/AMCZv/i672igDgv+FYeBf+gBH/4Ezf8AxdH/AArDwL/0AI//AAJm/wDi672igDgv+FYeBf8AoAR/+BM3/wAXV/S/AnhPRtcg1LTNIS1vod3lyieRtu5Sp4LEdCRXXUUAFfBB6mvvevgg9TQB9dfDD/kh2if9tv8A0fJXe1wXww/5Idon/bb/ANHyV3tAH5K6v8fdC1n/AILB+KtNvfj6/wAAdPaKXw0I7Xxjol19vn0a92hL3Tr6xdrJrlr+cQvFMXmjh6KQMfrVWe+k6XJdNPJpunyTltxka3UsT65xnNaFENKUYPdbvu+r+/psunW5NJ1ZTWz2Xbsvusr7u2r2SKK+b9O+Mnimf9pvStBvtB0KHwLrXi7UvCukTxTzf2kt3YWUl29xMrKI/JkNtdxhF5ASF9ziVlj5vxz8dPiD4O+OniLwZaeG/B3iVtmlrp9xZ3twq6NNqes22mWaajlDuMiTTXQWPaQtpIh+/HKzpxc3TUd5pOPndXX3ra/XTfQb0cr/AGXZ+Wtvwe/+R9aUV8OWX7TvxCn8Q+IbS48H+EVg8FaxYab4vlS8uM35vPEN5oyyWIK/u9iWn2orIXyZRDuG0zH7V1Oe/ttEnm0ywTU75QPKtnuBCJOQD85BxgZPTtS0aTT3s/k1dP0a1Q5RcZOL3Wj9VuvVdT8B/jl/yd38Qv8AsMy/zrymvT/jS80n7VfjuS5hFtcNqshliEm8I3GV3YGcHvivMK/0r4F/5JvL/wDrzS/9IifzxnX/ACMK/wDjl+bCiiivqTzArZ8Of8lB0L/sIwf+jFrGrZ8Of8lB0L/sIwf+jFrDFfwZ+j/I0pfGvU6z4wf8nafFH/sbtS/9K5a86r0X4wf8nafFH/sbtS/9K5a86rjyT/kXYf8AwR/9JRrjP48/V/mFFFFemcwV6/8AAD/k9T4Zf9h+3/8AQq8gr134Blh+2f8ADQou9xr0G1c4yd3TNeLxL/yKMV/17n/6Szsy7/eqX+Jfmfux4M/5JppP/XEV09eO+D9c8eD4c6WE8B2Tr5Iw3/CQoM/+Qq6X+3fH3/Qg2P8A4USf/Gq/zFP6MO9orgv7d8ff9CDY/wDhRJ/8ao/t3x9/0INj/wCFEn/xqgDvaK4L+3fH3/Qg2P8A4USf/GqP7d8ff9CDY/8AhRJ/8aoA72iuC/t3x9/0INj/AOFEn/xqj+3fH3/Qg2P/AIUSf/GqAO9orgv7d8ff9CDY/wDhRJ/8ao/t3x9/0INj/wCFEn/xqgDvaK4L+3fH3/Qg2P8A4USf/GqP7d8ff9CDY/8AhRJ/8aoA72iuC/t3x9/0INj/AOFEn/xqj+3fH3/Qg2P/AIUSf/GqAO9orgv7d8ff9CDY/wDhRJ/8ao/t3x9/0INj/wCFEn/xqgDvaK4L+3fH3/Qg2P8A4USf/GqP7d8ff9CDY/8AhRJ/8aoA72iuC/t3x9/0INj/AOFEn/xqj+3fH3/Qg2P/AIUSf/GqAO9orgv7d8ff9CDY/wDhRJ/8ao/t3x9/0INj/wCFEn/xqgDvaK4L+3fH3/Qg2P8A4USf/Gqv6Xq3i651yCDVPCFrpdi27zbpNZWcphSR8gjGcnA68Zz2oA66vgg9TX3vXwQepoA+uvhh/wAkO0T/ALbf+j5K72uC+GH/ACQ7RP8Att/6PkrvaACiiigDxu7+AXwvvPif4m8YSaTr8Ou69BPFfva+KtTt4I2nhjgmuLeCO4WK1unjijRrmBI5iAfn+Zs5Tfs0fCB9T8eXb6R4sdvGWoNqPiCFvHGsmCe9MlvIt5FCbvy7e5ja1tjFPAsckIiQRsgGK95op3dkuyt8u3p5D5n363+ff1PCrX9mv4NWWueGdSt/C+oLeaGyPA7eItQcX8kd3JfRy6gpnK6jKl3LLcpJeCZkmkeRSHYsfdaKKLu1v613E9Xc/n5+OX/J3fxC/wCwzL/OvKa9W+OX/J3fxC/7DMv868pr/SrgX/km8v8A+vNL/wBIifz1nX/Iwr/45fmwooor6k8wK2fDn/JQdC/7CMH/AKMWsatnw5/yUHQv+wjB/wCjFrDFfwZ+j/I0pfGvU6z4wf8AJ2nxR/7G7Uv/AErlrzqvRfjB/wAnafFH/sbtS/8ASuWvOq48k/5F2H/wR/8ASUa4z+PP1f5hRRRXpnMFev8AwA/5PU+GX/Yft/8A0KvIK9f+AH/J6nwy/wCw/b/+hV4vEv8AyKMV/wBe5/8ApLOzLv8AeqX+Jfmfut4M/wCSaaT/ANcRXT1zHgz/AJJppP8A1xFdPX+Yp/RgUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABXwQepr73r4IPU0AfXXww/5Idon/bb/wBHyV3tcF8MP+SHaJ/22/8AR8ld7QAUUUUAcHZ/E/wBqHxovfh5Z+KdLuPGdoHFxpiMd6ukcUrxhsbDKkc8MjRhi6pLGzKFYE0Lj4yfCu1vPHFvL4+8MG48HSW0XiiKO9WRtLluWK28MoXJE0jDakX32YqAuWUHxGX4U/F20/aCk1jTbT4dXnhjQPE+r+LfC09z4gvIb3Ub++sJbUWN7ELSRYLdGurlvPjklbakIEIw1Y3jf4N/GTxH+0x8VPFmm6Z8LrfRNStvCc/hv7T4mvfPuLrw/q8uprHdxLYbYI7k3MkZkSSYwmNH8ubeVTSnCLhBydm0m+tndc33K9l9q2g7e/JdE9PNdPS+/ls9T3W3+Pfwdur/AMP2sHxA0GS51mVYrKLewZZGunskjmBX/R3a6jktlWbYWnRogC6lR6ne31lpumS3uo3lrYWcWPMnuZVjjTJAGWYgDkgfjXwdp/7N3xch8Xa3dXU3w2Wz8earp2p+M2h1a8aXQGsvEV7rSw2ANsBfB0vPI8yQ2pR0M2x9/kr97zQw3Fu0NxFHPE33kkUMp+oNR9lPr/Wnyel/tb2Q5pKbUXddPNd/n23W2p/Px8a5obj9rDx7cW8sc8EmryPHJGwZXU4III4IPrXl1eqfG9Ej/a2+ICRqqIusShVUYAHHAryuv9KuBf8Akm8v/wCvNL/0iJ/PGdf8jCv/AI5fmwooor6k8wK2fDn/ACUHQv8AsIwf+jFrGrZ8Of8AJQdC/wCwjB/6MWsMV/Bn6P8AI0pfGvU6z4wf8nafFH/sbtS/9K5a86r0X4wf8nafFH/sbtS/9K5a86rjyT/kXYf/AAR/9JRrjP48/V/mFFFFemcwV698AmVP20Pho7sFVdegJJOABuryGvYf2fkEn7avwzUlFX+3oCxc4AAOTmvE4lf/AAkYv/r3P/0lnZl3+90v8S/M/avwd458FJ8N9KV/GHhZWEIyDq0II/8AHq4D4s/Fa2tde+Hnhnwj8UPBnhObxDq11De6zLNa3bwRQafdXKpGkkgQO8kUeSwYeWsoAVirrzfh/wDaD/Zx0zwhY2N14u8MNcRRhXKabIQT9fKqt4p+MP7HnjnwqdC8ayfDrxfohlWU6frXhoXluXX7r+XLCy7h2OMiv86Z8E8Qyi19Rq/+C5/5f8Psfvsc4wKf8aP3r/M4G+/aX1vxP+zh8HNX0jx94B+HniTxD8Mb3xhrtzcC3uora8trKymWwMUkwKI8l4Xbkv5UDKroW8wZPi79pbxd4ftvFfirw/428N67Z6X8LH8S3/h2+t7XFhql6YxpllHIrxNKI/LvXnV5FZVWDLJ5m4d/q/xE/Yg8QW7w69pfwl1uJ9Ri1J0v/B8U4a7ihSCO5IeA5mWKOONZPvBEVQcACt9/jh+yTJBrsT6h4DeLWyTrKN4fyNRJiWA+ePJ/e/uk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4.0000000 0.3333333 0 <session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>555</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>298</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>076</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>047</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>014</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>01</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi><mo>=</mo><mn>1</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>c</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>d</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>e</mi><mo>+</mo><mn>6</mn><mo>*</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mn>1</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mo>(</mo><mn>2</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mo>(</mo><mn>3</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>d</mi><mo>*</mo><mo>(</mo><mn>4</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>e</mi><mo>*</mo><mo>(</mo><mn>5</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>f</mi><mo>*</mo><mo>(</mo><mn>6</mn><mo>-</mo><mi>me</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>precision</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi><mo>=</mo><msqrt><mi>var</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]> Question 39 Household Size

The histogram shows the distribution of household sizes in the United States for a recent year.

 

  1. Find the mean of the probability distribution to three significant digits.
    {#1}

  2. Find the variance of the probability distribution to three significant digits.
    {#2}

  3. Find the standard deviation of the probability distribution to three significant digits.
    {#3}

  4. Find the expected value of the probability distribution to three significant digits.
    {#4}
]]> 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The histogram shows the distribution of carpooling by the number of cars per household.

 

  1. Find the mean of the probability distribution to three significant digits.
    {#1}

  2. Find the variance of the probability distribution to three significant digits.
    {#2}

  3. Find the standard deviation of the probability distribution to three significant digits.
    {#3}

  4. Find the expected value of the probability distribution to three significant digits.
    {#4}
]]> 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4.0000000 0.3333333 0 <session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>29</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>25</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>17</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>16</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>13</mn></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.59</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.92</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sd</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.39</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]> Question 45 In American roulette, the wheel has the 38 numbers

00, 0, 1, 2, 3, ..., 34, 35, and 36

marked on equally spaced slots.  If a player bets $1 on a number and wins, then the player keeps the dollar and receives an additional 35 dollars.  Otherwise, the dollar is lost.  Find the expected net gain to the player for one play of the game to the nearest cent.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»E«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«/math» ${#1}

]]> 1.0000000 0.3333333 0 ]]> Question 46 A charity organization is selling $4 raffle tickets as part of a fund-raising program.  The first prize is a boat valued at $3150, and the second prize is a camping tent valued at $450.  The remaining 15 prizes are $25 gift certificates.  The number of tickets sold is 5000.  Find the expected net gain to the player for one play of the game to the nearest cent.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»E«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«/math» ${#1}

]]> 1.0000000 0.3333333 0 ]]>