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, if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean is approximately normal if n > 30. This is true regardless of the underlying population distribution. Thus, option B is the correct choice. Option A is incorrect because it suggests that the sampling distribution is not normal if n < 30, which is untrue. Option C is incorrect because it suggests that the population must be normal for the sampling distribution to be approximately normal, which is also untrue. Option D is incorrect because one of the other choices is correct.

The Central Limit Theorem States That, If a Random Sample