Imagine a large bimodal population of test scores with a mode at 33 and a mode at 66. Suppose you drew many random samples of 30 students and calculated the mean of each sample. Finally, you arranged all these means into a frequency distribution. You would expect the distribution to be
A) bimodal
B) rectangular
C) normal
D) any of the other alternatives, depending on how many were in the population.

Question

Quizplus · Accepted Answer

According to the Central Limit Theorem, regardless of the shape of the population distribution, the sampling distribution of the sample mean will approach a normal distribution as the sample size becomes large. In this case, with many samples of size 30, the distribution of the means is expected to be normal, not reflecting the bimodal nature of the population.

Imagine a Large Bimodal Population of Test Scores with a Mode