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.

Central Limit Theorem

A statistical theory that states that, given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population, and the samples will be distributed approximately normally.

Normal Probability Distribution

A type of continuous probability distribution that is symmetrical around its mean, representing how random variables are distributed in many natural phenomena.