Question 211:

1

The Central limit theorem shows that as sample sizes get larger, the sampling distribution of the mean begins to resemble the normal distribution. This especially becomes the case as the sample size gets above 30. This is the case regardless of what the shape of the probability distribution from which the samples are taken.

Population shape is of concern since if a population or sample is not normally distributed (say it is positively skewed) the mean will be affected and not be an accurate representation of the center of the distribution. Positively skewed populations are things like salaries of employees, home values (very large values skew the whole distribution to the right).

Let say we sampled 10 employees from a company and took their mean salary. We then repeated this sample another 40 times so we had 40 mean salaries (each mean is made up of 10 employee salaries). This sample of 40 means would have a roughly normally distributed shape according to the central limit theorem.