The central limit theorem states that:
A) even with populations that have dramatically non-normal distributions, the sampling distributions of the mean will be increasingly normal in shape as sample sizes increase.
B) the sampling distributions of the mean will reflect the shape of the underlying population, such that normally distributed samples can be assumed to come from a normally distributed population.
C) the sampling distributions of the mean will reflect the shape of the underlying population only for large sample sizes, such that populations with drastically non-normal distributions will yield sampling distributions that are normal for small to moderate sample sizes.
D) even with populations that have dramatically non-normal distributions, the sampling distributions of the mean will be increasingly normal in shape as sample sizes decrease.

Question

Quizplus · Accepted Answer

The central limit theorem states that the sampling distribution of the mean will approach a normal distribution as the sample size increases, even for populations that do not have a normal distribution. This means that for sufficiently large sample sizes, the shape of the population distribution becomes less important and normality can be assumed.

The Central Limit Theorem States That