Questions: According to the central limit theorem, the sampling distribution of the sample means is approximately normal if Multiple Choice the underlying population is not normal. the sample size n ≥ 30 both the underlying population is not normal and the sample size n ≥ 30 are correct. the standard deviation of the population is large.

Solution Steps

To determine the correct answer, we need to understand the central limit theorem (CLT). The CLT states that the sampling distribution of the sample mean will be approximately normal if the sample size is sufficiently large, typically \( n \geq 30 \), regardless of the shape of the population distribution. Therefore, the correct choice is the one that mentions the sample size \( n \geq 30 \).

The central limit theorem (CLT) states that the sampling distribution of the sample mean will be approximately normal if the sample size \( n \) is sufficiently large, typically \( n \geq 30 \). This holds true regardless of the underlying population distribution.

We have the following options to consider:

1. The underlying population is not normal.
2. The sample size \( n \geq 30 \).
3. Both the underlying population is not normal and the sample size \( n \geq 30 \) are correct.
4. The standard deviation of the population is large.

Among these options, the second option directly aligns with the requirement of the CLT.

The correct answer is the one that states the condition for the sampling distribution to be approximately normal, which is \( n \geq 30 \). Therefore, the correct choice is option 2.

Final Answer