The correct answer is:

"Yes, the sampling distribution is approximately normal because the sample size is greater than 30."

Explanation:

According to the Central Limit Theorem (CLT), if the sample size is sufficiently large (typically $n \geq 30$), the sampling distribution of the sample mean will be approximately normal, regardless of the population's distribution. In this case, since the sample size $n = 40$, which is greater than 30, the sampling distribution can be considered approximately normal.

Even if the population itself is not normally distributed, the CLT ensures that the sample mean's distribution approaches normality as the sample size increases.

• The second option (because the population is normally distributed) would also be correct if it were stated explicitly that the population is normal, but it isn’t given.
• The other two options are incorrect because they misunderstand the requirements of the Central Limit Theorem and the conditions for normality.

Would you like more details or have any other questions?

Related Questions:

1. What is the Central Limit Theorem, and why is it important in statistics?
2. How does the sample size affect the shape of the sampling distribution?
3. What happens to the sampling distribution if the sample size is less than 30 and the population is not normal?
4. How do we estimate the standard error of the mean in a sample?
5. What is the impact of increasing the sample size on the sampling distribution?

Tip:

Always check whether the sample size meets the criteria of the Central Limit Theorem when determining if a sampling distribution is approximately normal.