Answer: [tex]\mu_{\hat{p}}=0.67[/tex]
[tex]\sigma_{\hat{p}}=0.029[/tex]
Step-by-step explanation:
The mean and standard deviation of the sampling distribution of the sample proportions is given by :-
[tex]\mu_{\hat{p}}=p[/tex]
[tex]\sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}[/tex] , where n is the sample size and p is the population proportion.
Given : p= 0.67 and n= 256
Then, the mean and standard deviation of the sampling distribution of the sample proportions is given by :-
[tex]\mu_{\hat{p}}=0.67[/tex]
[tex]\sigma_{\hat{p}}=\sqrt{\dfrac{0.67(1-0.67)}{256}}\\\\=0.0293882948638\approx0.029[/tex]
