Answer with explanation:
We are given that [tex]\hat{p}=0.91[/tex]
Sample size : [tex]n=144[/tex]
The mean of the sampling distribution of the sample proportions is given by :-
[tex]\mu_{\hat{p}}=p=0.91[/tex]
The mean of the sampling distribution of the sample proportions is 0.91
The standard deviation of the sampling distribution of the sample proportions :
[tex]\sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}\\\\=\sqrt{\dfrac{0.91(1-0.91)}{144}}=0.0238484800354\approx0.0238[/tex]
Hence, the standard deviation of the sampling distribution of the sample proportions is 0.0238
