8. Discuss how a sampling distribution of means derived from numerous large samples drawn from a skewed population will form a normal distribution.

Answer 1

According to the Central Limit Theorem, As the sample size gets large enough, the sampling distribution of the mean is approximately normally distributed. This is true regardless of the shape of the distribution of the individual values in the population.

As a general rule, statisticians have found that for many population distributions, when the sample size is at least 30, the sampling distribution of the mean is approximately normal..

In the case in which the distribution of a variable is extremely skewed, you may need sample sizes larger than 30 to insure normality in the sampling distribution of the mean.