The Central Limit Theorem states that, if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean : A) is approximately normal if n 30. C) is approximately normal if the underlying population is normal. D) None of these choices.

Question

The Central Limit Theorem states that, if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean  :
A) is approximately normal if n < 30. 
B) is approximately normal if n > 30. 
C) is approximately normal if the underlying population is normal. 
D) None of these choices.

Quizplus · Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean is approximately normal, regardless of the distribution of the population, as long as the sample size is large enough (usually n > 30 or n > 40). Therefore, the correct choice is B, which states that the sampling distribution of the sample mean is approximately normal if n > 30. Option A is incorrect because n < 30 is usually considered small and may not meet the conditions of the Central Limit Theorem. Option C is incorrect because the underlying population does not have to be normal for the Central Limit Theorem to apply. Option D is incorrect because one of the choices (B) is the correct answer.

The Central Limit Theorem States That, If a Random Sample