Question

Which of the following best answers whether the sample mean heights of adult women from a sample of size 30 will be approximately normally distributed?

A) Yes, since heights are approximately normally distributed.
B) No, since heights are approximately normally distributed.
C) Yes, since 30 is less than 5% of the population.
D) Yes, since the sample size is at least 30.

Answer 1

Option D (Yes, since the sample size is at least 30) is the correct answer since the Central Limit Theorem states that the distribution of sample means will be approximately normal if the sample size is large enough.

Step-by-step explanation:

The best answer to whether the sample mean heights of adult women from a sample of size 30 will be approximately normally distributed is D) Yes, since the sample size is at least 30. According to the Central Limit Theorem, the distribution of sample means will be normally distributed if the sample size is large enough (usually n ≥ 30) despite the shape of the population distribution. This is why option D is the best choice as it reflects the concept that when the sample size is large, the sampling distribution of the mean will approximate a normal distribution.