Suppose a simple random sample of size $n=75$ is obtained from a population whose size is $N=30,000$ and whose population proportion with a specified characteristic is $p=0.6$. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). D. Not normal because $n \leq 0.05 \mathrm{~N}$ and $n p(1-p) \geq 10$. Determine the mean of the sampling distribution of $\hat{p}$. $\mu_{p}=0.6$ (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of $\hat{p}$. $\sigma_{\hat{p}}=\square$ (Round to six decimal places as needed.)

Step 1 ：We are given a simple random sample of size \(n=75\) obtained from a population of size \(N=30,000\) with a population proportion \(p=0.6\).

Step 2 ：We are asked to find the mean and standard deviation of the sampling distribution of the proportion.

Step 3 ：The mean of the sampling distribution of the proportion, also known as the expected value of \(\hat{p}\), is equal to the population proportion \(p\). So, \(\mu_{p}=0.6\).

Step 4 ：The standard deviation of the sampling distribution of the proportion is given by the formula: \[\sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n} \cdot \frac{N-n}{N-1}}\] where \(p\) is the population proportion, \(n\) is the sample size, and \(N\) is the population size.

Step 5 ：Substituting the given values \(p = 0.6\), \(n = 75\), and \(N = 30,000\) into the formula, we can calculate the standard deviation.

Step 6 ：The calculated standard deviation of the sampling distribution of \(\hat{p}\) is approximately 0.056499.

Step 7 ：So, the final answer is: The standard deviation of the sampling distribution of \(\hat{p}\) is \(\boxed{0.056499}\).