Final answer:
The Central Limit Theorem states that the sample means of large-sized samples follow a normal distribution regardless of the shape of their population distributions.
Step-by-step explanation:
The Central Limit Theorem states that the sample means of large-sized samples will follow a normal distribution regardless of the shape of their population distributions.
The Central Limit Theorem tells us that if samples of sufficient size are drawn from a population, the distribution of sample means will be normal, even if the distribution of the population is not normal. As the sample size increases, the sample means form their own normal distribution (the sampling distribution).
For example, if you keep drawing larger and larger samples and calculating their means, the sample means form their own normal distribution, with the same mean as the original distribution and a variance that equals the original variance divided by the sample size.