The question provided is about the conditions under which the sampling distribution of the sample mean, $\bar{x}$, will be approximately normally distributed, even when the population distribution is not normal.

The correct answer here relies on the Central Limit Theorem (CLT), which states that the sampling distribution of the sample mean $\bar{x}$ will tend to be normally distributed as the sample size $n$ becomes sufficiently large, regardless of the population's original distribution.

So the correct answer is:

"when $n$ is sufficiently large."

This is because the Central Limit Theorem implies that for large sample sizes, the sampling distribution of the mean will approximate a normal distribution.

Would you like more detailed information on the Central Limit Theorem or its applications?

Related Questions

1. What is the Central Limit Theorem, and why is it important?
2. How large does $n$ need to be for the Central Limit Theorem to apply?
3. What happens to the sampling distribution of $\bar{x}$ when the population is already normally distributed?
4. How does the standard error of the mean change as $n$ increases?
5. What is the role of kurtosis in determining the shape of the sampling distribution?

Tip

For many practical purposes, a sample size of $n \geq 30$ is often considered "sufficiently large" for the Central Limit Theorem to hold, though this can vary based on the population's skewness and kurtosis.