The fact that the sampling distribution of the sample mean 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 there are tables of areas for the normal distribution
C) assumption that the population has a normal distribution
D) normal probability theorem

Question

Quizplus · Accepted Answer

The central limit theorem is a fundamental concept in statistics that states that the mean of a sufficiently large sample from any population is approximately normally distributed. This theorem is the reason why the sampling distribution of the sample mean can be approximated by a normal probability distribution when the sample size is large. The other options (B, C, and D) are not correct because the fact that there are tables of areas for the normal distribution or the assumption that the population has a normal distribution does not imply that the sample mean distribution is normal. Also, there is no such thing as the "normal probability theorem."

The Fact That the Sampling Distribution of the Sample Mean