The annual salary for one particular occupation is normally distributed, with a mean of about $\$ 140,000$ and a standard deviation of about $\$ 15,000$. Random samples of 28 are drawn from this population, and the mean of each sample is determined. Find the mean and standard deviation of the sampling distribution of these sample means. Then, sketch a graph of the sampling distribution
The mean is $\mu_{\bar{x}}=\square$, and the standard deviation is $\sigma_{\bar{x}}=$
(Round to the nearest integer as needed. Do not include the $\$$ symbol in your answers.)

Step 1 ：The problem provides us with the following information: the mean annual salary for a particular occupation is normally distributed, with a mean of about $140,000 and a standard deviation of about $15,000. We are drawing random samples of 28 from this population and determining the mean of each sample.

Step 2 ：The mean of the sampling distribution of the sample means is equal to the population mean. Therefore, the mean of the sampling distribution is $140,000.

Step 3 ：The standard deviation of the sampling distribution of the sample means, also known as the standard error, is equal to the population standard deviation divided by the square root of the sample size. In this case, the sample size is 28. Therefore, the standard deviation of the sampling distribution is \(\frac{15000}{\sqrt{28}}\).

Step 4 ：Calculating the above expression gives us a standard deviation of approximately 2834.733547569204.

Step 5 ：Rounding to the nearest integer, we get a standard deviation of 2835.

Step 6 ：Final Answer: The mean of the sampling distribution of the sample means is \(\boxed{140000}\), and the standard deviation is \(\boxed{2835}\).