Assume that a test is given to a large number of people but

Assume that a test is given to a large number of people but we do not yet know their scores or the shape of the score distribution. Can we be sure that the sampling distribution of the mean for this test will be normally distributed? why? or why not?

Solution

Yes, because of central limit theorem, which say that sampling distribution of mean is approximately normal if sample size is large (atleast 30) for any population (with finite mean and variance)