The central limit theorem states that ______.
A)as the size of a sample gets larger and larger,its distribution approaches the normal distribution only if the underlying population from which the samples were collected is normally distributed
B)as the size of a sample gets smaller and smaller,its distribution approaches the normal distribution,if the underlying population from which the samples were collected is not normally distributed
C)as the size of a sample gets larger and larger,its distribution approaches the normal distribution,even if the underlying population from which the samples were collected is not normally distributed
D)as the size of a population gets larger and larger,its distribution approaches the normal distribution,even if the population is not normally distributed to begin with

Question

Quizplus · Accepted Answer

The central limit theorem states that as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the underlying population distribution, as long as the sample is random and independent. Therefore, option C is the correct statement among the given choices.

The Central Limit Theorem States That ______