In a report prepared by the Economic Research Department of

) In a report prepared by the Economic Research Department of a major bank, the department manager states that the average annual family income on Metropolis is $48,432 and the standard deviation is $1500. In order to test the claim, a manager in a different department in the bank randomly selects 50 families from Metropolis. The manager then states that since there are more than 30 observations in the random sample, the random sample of family income values follows (approximately) a Normal distribution. Do you agree with the manager? Please explain.

Solution

Yes, I agree with the manager because we can use central limit theorem to be approximately normal distribution, regardless of the underlying distribution.