(Solved): Describe the sampling distribution of \( \hat{p} \). Assume the size of the population is 30,000 \ ...

Describe the sampling distribution of \( \hat{p} \). Assume the size of the population is 30,000 \[ n=800, p=0.2 \] Choose the phrase that best describes the shape of the sampling distribution of \( \hat{p} \) below. A. Not normal because \( n \leq 0.05 \mathrm{~N} \) and \( n p(1-p) \geq 10 \). B. Approximately normal because \( n \leq 0.05 \mathrm{~N} \) and \( n p(1-p) \geq 10 \). C. Not normal because \( n \leq 0.05 \mathrm{~N} \) and \( n p(1-p)<10 \). D. Approximately normal because \( n \leq 0.05 \mathrm{~N} \) and \( n p(1-p)<10 \). Determine the mean of the sampling distribution of \( \hat{p} \). \[ \mu_{\hat{p}}= \] (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of \( \hat{p} \). \( \sigma_{\hat{n}}= \) (Round to three decimal places as needed.)