Describe the sampling distribution of $\hat{p}$. Assume the size of the population is 25,000.
n = 1000, p = 0.415
Describe the shape of the sampling distribution of $\hat{p}$. Choose the correct answer below.
A. The shape of the sampling distribution of $\hat{p}$ is not normal because $n \le 0.05N$ and $np(1-p) \ge 10$.
B. The shape of the sampling distribution of $\hat{p}$ is not normal because $n \le 0.05N$ and $np(1-p) < 10$.
C. The shape of the sampling distribution of $\hat{p}$ is approximately normal because $n \le 0.05N$ and $np(1-p) \ge 10$.
D. The shape of the sampling distribution of $\hat{p}$ is approximately normal because $n \le 0.05N$ and $np(1-p) < 10$.
Determine the mean of the sampling distribution of $\hat{p}$.
$\mu_{\hat{p}} = 0.415$ (Round to three decimal places as needed.)
Determine the standard deviation of the sampling distribution of $\hat{p}$.
$\sigma_{\hat{p}} = \text{ }$ (Round to three decimal places as needed.)