Discrete Probability Distributions/Probability Distributions 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

«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}

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}
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}
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}
Find the mean to 3 significant digits.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#956;«/mi»«mo»=«/mo»«/math» {#10}
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}
Find the standard deviation to 3 significant digits.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#963;«/mi»«mo»=«/mo»«/math» {#12}

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