A politician takes an SRS of 757575 citizens in a county to see what proportion of citizens sampled are satisfied with their standard of living. Suppose that 80\%80%80, percent of the 118{,}000118,000118, comma, 000 citizens in the county are satisfied with their standard of living. What are the mean and standard deviation of the sampling distribution of the proportion of citizens who are satisfied with their standard of living?
μ
p
^
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​

σ
p
^
​

​

​

=(75)(0.8)
=
75(0.8)(1−0.8)
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​

(Choice B)
B
\begin{aligned} \mu_{\hat p}&=0.8 \sigma_{\hat p}&=\sqrt{75(0.8)(1-0.8)} \end{aligned}
μ
p
^
​

​

σ
p
^
​

​

​

=0.8
=
75(0.8)(1−0.8)
​

​

(Choice C)
C
\begin{aligned} \mu_{\hat p}&=(75)(0.8) \sigma_{\hat p}&=\sqrt{\dfrac{0.8(1-0.8)}{75 }} \end{aligned}
μ
p
^
​

​

σ
p
^
​

​

​

=(75)(0.8)
=
75
0.8(1−0.8)
​

​

​

(Choice D)
D
\begin{aligned} \mu_{\hat p}&=0.8 \sigma_{\hat p}&=\sqrt{\dfrac{0.8\left(1-0.8 \right)}{75}} \end{aligned}
μ
p
^
​

​

σ
p
^
​

​

​

=0.8
=
75
0.8(1−0.8)
​

​

​