The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size is large is based on the
A) central limit theorem.
B) fact that we have tables of areas for the normal distribution.
C) assumption that the population has a normal distribution.
D) none of these alternatives is correct.

Question

Quizplus · Accepted Answer

The central limit theorem states that, under certain conditions, the sampling distribution of sample means will be approximately normal, regardless of the shape of the original population distribution. Therefore, option A is the correct choice. Option B is incorrect because the fact that we have tables of areas for the normal distribution does not relate to the reason why the sampling distribution of sample means can be approximated by a normal distribution. Option C is also incorrect because the assumption that the population has a normal distribution is not necessary for the central limit theorem to hold.

The Fact That the Sampling Distribution of Sample Means Can