A large population is bi-modal (like you'd get if you included the heights of both men and women in the same distribution). Samples of size 40 are drawn and a sampling distribution of the mean values of these samples is constructed. What's the most likely shape of the sampling distribution of the sample mean?
A. Bi-modal, since the sample size isn't large enough to use the Central Limit Theorem
B. Bi-modal, as predicted by the Central Limit Theorem
C. Symmetric but clearly not normal, as predicted by the Central Limit Theorem
D. Approximately normal, as predicted by the Central Limit Theorem
E. Skewed either to the left or to the right
27
D. Approximately normal, as predicted by the Central Limit Theorem
The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean will approach a normal distribution, regardless of the shape of the population distribution. Therefore, even though the population distribution is bi-modal, the sampling distribution of the sample mean will be approximately normal with a sample size of 40.