The Central Limit Theorem is important in statistics because
A) for any sized sample, it says the sampling distribution of the sample mean is approximately normal.
B) for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size.
C) for a large n, it says the population is approximately normal.
D) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that as the sample size (n) becomes large, the sampling distribution of the sample mean will approach a normal distribution, regardless of the population's distribution shape. This is why it's a fundamental concept in statistics, allowing for the application of normal probability to problems involving sample means for large samples.

The Central Limit Theorem Is Important in Statistics Because