The mean of the sampling distribution of sample means is equal to the mean of the population from which the samples are drawn.

Given:

• Population mean (μ) = 40
• Sample size (n) = 25
• Population standard deviation (σ) = 7.5

The mean of the sampling distribution of sample means (often denoted as $\mu_{\bar{x}}$) is simply the population mean, regardless of the sample size.

Therefore, the mean of the sampling distribution of sample means is:

$\mu_{\bar{x}} = 40$

So, the correct answer is:

D. 40

Would you like further clarification, or do you have any other questions?

Here are five related questions to explore:

1. What is the standard error of the sampling distribution of sample means in this case?
2. How does increasing the sample size affect the standard error?
3. What is the Central Limit Theorem and how does it apply to sampling distributions?
4. How do you calculate the probability of a sample mean falling within a certain range?
5. What assumptions must be met for the sampling distribution of sample means to be normally distributed?

Tip: The standard error of the mean decreases as the sample size increases, which means larger samples tend to give more accurate estimates of the population mean.