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In Metro Vancouver, the proportion of households that were renters in 2011 was 0.34. Imagine you constructed a sampling distribution by repeatedly taking samples of size 500. What are the mean and standard deviation of this sampling distribution?

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JeanaShupp

Answer: [tex]\mu=170\ ;\ \sigma=10.59[/tex]

Step-by-step explanation:

Given : The proportion of households that were renters in 2011 : p= 0.34

Sample size : n= 500

The mean and standard deviation for binomial distribution is given by :-

[tex]\mu=np\\\\\sigma=\sqrt{np(1-p)}[/tex]

Then , the  mean and standard deviation of the given sampling distribution :-

[tex]\mu=500(0.34)=170\\\\\sigma=\sqrt{500(0.34)(1-0.34)}\approx10.59[/tex]

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