Describe the sampling distribution of $\hat{p}$. Assume the size of the population is 25,000 . \[ n=200, p=0.4 \] Determine the mean of the sampling distribution of $\hat{p}$ $\mu_{p}=4$ (Round to one decimat place as needed.) Determine the standard deviation of the sampling distribution of $\hat{p}$. $\sigma_{\hat{p}}=\square$ (Round to three decimal places as needed)

Step 1 ：The problem is asking for the mean and standard deviation of the sampling distribution of $\hat{p}$. The mean of the sampling distribution of $\hat{p}$ is equal to the population proportion, p.

Step 2 ：Given that p = 0.4, the mean of the sampling distribution of $\hat{p}$ is $\boxed{0.4}$.

Step 3 ：The standard deviation of the sampling distribution of $\hat{p}$ can be calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, where n is the sample size.

Step 4 ：Given that p = 0.4 and n = 200, we can substitute these values into the formula to calculate the standard deviation.

Step 5 ：The standard deviation of the sampling distribution of $\hat{p}$ is approximately 0.034641016151377546.

Step 6 ：Rounding to three decimal places, the standard deviation of the sampling distribution of $\hat{p}$ is $\boxed{0.035}$.