Part 1 of 2
Points: 0 of 1
Determine $\mu_{\bar{x}}$ and $\sigma_{\bar{x}}$ from the given parameters of the population and sample size.
\[
\mu=42, \sigma=24, n=40
\]
\[
\mu_{\bar{x}}=
\]

Step 1 ：The mean of a sampling distribution of sample means, often denoted as \(\mu_{\bar{x}}\), is equal to the population mean, \(\mu\). So in this case, \(\mu_{\bar{x}}\) should be 42.

Step 2 ：The standard deviation of a sampling distribution of sample means, often denoted as \(\sigma_{\bar{x}}\), is equal to the population standard deviation, \(\sigma\), divided by the square root of the sample size, \(n\). So in this case, \(\sigma_{\bar{x}}\) should be \(\frac{24}{\sqrt{40}}\).

Step 3 ：Simplify \(\sigma_{\bar{x}}\) to get the final answer. \(\sigma_{\bar{x}} = \frac{24}{\sqrt{40}} = 3.8\) (rounded to one decimal place)

Step 4 ：Final Answer: The mean of the sampling distribution of sample means is \(\boxed{42}\) and the standard deviation of the sampling distribution of sample means is \(\boxed{3.8}\).