Answer to Question #338041 in Statistics and Probability for Maw

Question

A certain population has a variance of 2.5, and a sample size of 4 is used to obtain the sampling distribution of the sample mean of this population. What is the variance of the sampling distribution of the sample mean?

Write your answer as a fraction in lowest terms.

Answer 1

$$Var(\bar{X})=\sigma_{\bar{X}}^2=\dfrac{\sigma^2}{n}=\dfrac{2.5}{4}=\dfrac{5}{8}$$