Given that the population distribution is not normal but the sample size is large, the correct answer is:

Same mean but different shape and standard deviation.

This is because, according to the Central Limit Theorem (CLT), for a sufficiently large sample size, the sampling distribution of the sample mean will tend to be approximately normal (even if the population distribution is not normal). However, the standard deviation of the sampling distribution (often called the standard error) is different from the population standard deviation and is calculated as the population standard deviation divided by the square root of the sample size. The shape of the sampling distribution will be normal, even though the population distribution was not.

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. What is the Central Limit Theorem and why is it important in statistics?
2. How do you calculate the standard error of the mean?
3. What happens to the shape of the sampling distribution as the sample size increases?
4. How does the standard deviation of a population affect the standard error of the mean?
5. What conditions must be met for the Central Limit Theorem to apply?
6. How does a small sample size affect the sampling distribution if the population is not normal?
7. What are the differences between population standard deviation and standard error?
8. Can the Central Limit Theorem be applied to proportions as well as means?

Tip: The Central Limit Theorem is a fundamental concept in statistics that justifies using the normal distribution as an approximation for the sampling distribution of the mean, even when the population distribution is not normal.