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 \(\boxed{3.8}\).