The Central Limit Theorem (CLT) implies that:
A)the population will be approximately normal if n ≥ 30.
B)repeated samples must be taken to obtain normality.
C)the distribution of the mean is approximately normal for large n.
D)the mean follows the same distribution as the population.

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that for large enough sample sizes (n≥30), the distribution of the sample mean will be approximately normal, regardless of the underlying population distribution. This is why the mean is often used as a point estimate for population parameters. The theorem does not imply that the population will be normal or that repeated samples must be taken to obtain normality. Additionally, while the mean can be used as an estimate of the population parameter, it does not necessarily follow the exact same distribution as the population.

The Central Limit Theorem (CLT) Implies That