The statement is False.

Here's why:

• The sampling distribution of the sample mean can be approximately normal even if the population from which the sample is drawn is not normally distributed. This is guaranteed by the Central Limit Theorem (CLT), which states that for sufficiently large sample sizes (typically $n \geq 30$), the sampling distribution of the sample mean will approximate a normal distribution, regardless of the population's distribution.
• However, if the population itself is normally distributed, the sampling distribution of the sample mean will always be normal, even for small sample sizes.

Would you like more details on the Central Limit Theorem or any other aspects of this concept?

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Here are 5 related questions to deepen your understanding:

1. What is the Central Limit Theorem (CLT), and why is it important?
2. How large does a sample size need to be for the CLT to apply?
3. If a population is not normally distributed, what does the sampling distribution of the sample mean look like for small sample sizes?
4. How does the shape of the population distribution affect the sample mean distribution for small samples?
5. What are some practical applications of the Central Limit Theorem in statistics?

Tip: Always check whether the sample size is large enough when applying the Central Limit Theorem to ensure the sampling distribution is approximately normal.