Discrete Probability Distributions/Binomial Distributions Question 26 No Trouble Sleeping

imgres.jpg

On in four adults say he or she has no trouble sleeping at night.  You randomly select five adults and ask each if he or she has no trouble sleeping at night.

  1. Construct a binomial probability distribution to three significant figures.
    «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»
    {#1} {#2}
    {#3} {#4}
    {#5} {#6}
    {#7} {#8}
    {#9} {#10}
    {#11} {#12}
  2. The graph of the distributions is
    {#13}

  3. Find the mean, variance, and standard deviation of the binomial distribution.
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#956;«/mi»«mo»=«/mo»«/math» {#14}
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»§#963;«/mi»«mn»2«/mn»«/msup»«mo»=«/mo»«/math» {#15}
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#963;«/mi»«mo»=«/mo»«/math» {#16}

  4. What values of the random variable x would be considered unusual?
    {#17}
]]> 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 17.0000000 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>n</mi><mo>=</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</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>a</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mn>0</mn></apply><mo>*</mo><msup><mi>p</mi><mn>0</mn></msup><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>p</mi></mrow></mfenced><mrow><mi>n</mi><mo>-</mo><mn>0</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mn>1</mn></apply><mo>*</mo><msup><mi>p</mi><mn>1</mn></msup><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>p</mi></mrow></mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mn>2</mn></apply><mo>*</mo><msup><mi>p</mi><mn>2</mn></msup><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>p</mi></mrow></mfenced><mrow><mi>n</mi><mo>-</mo><mn>2</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mn>3</mn></apply><mo>*</mo><msup><mi>p</mi><mn>3</mn></msup><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>p</mi></mrow></mfenced><mrow><mi>n</mi><mo>-</mo><mn>3</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mn>4</mn></apply><mo>*</mo><msup><mi>p</mi><mn>4</mn></msup><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>p</mi></mrow></mfenced><mrow><mi>n</mi><mo>-</mo><mn>4</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mn>5</mn></apply><mo>*</mo><msup><mi>p</mi><mn>5</mn></msup><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>p</mi></mrow></mfenced><mrow><mi>n</mi><mo>-</mo><mn>5</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>p</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>p</mi><mo>*</mo><mfenced><mrow><mn>1</mn><mo>-</mo><mi>p</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msqrt><mi>v</mi></msqrt></math></input></command></group></library></session>]]>