A community has five families whose annual incomes are 1 2 3

A community has five families whose annual incomes are 1, 2, 3, 4, and 5 respectively. Suppose a survey is to be made to two of the five families and the choice of the two is random. Find the sampling distribution of the sample mean of the family income. Give your reasoning clearly

Solution

The population here is normal. Hence the sampling distirbution is normal wih mean xbar and sd var/n.

This follows from the central limit theorem.