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