As the size of the sample increases what happens to the shap

As the size of the sample increases, what happens to the shape of the distribution of sample means?

It cannot be predicted in advance

It is negatively skewed

It approaches a normal distribution

It is positively skewed

Solution

Centra limit theorem states that a population with a finite mean and a finite non zero variance,the sampling distribution of the mean approaches a normal distribution with same mean value and variance reduced to a value of initial variance divided by sample size N,( variance new = variance initial / N).

As the size of the sample increases the shape of the distribution approaches normal distribution.