A random sample of 121 checking accounts at a bank showed an

A random sample of 121 checking accounts at a bank showed an average daily balance of $280. The population standard deviation is known to be $60. Is it necessary to know anything about the shape of the distribution of the account balances in order to make an interval estimate of the mean of all the account balances?

Solution

No. According to the central limit theorem, for a sufficiently large number of iterates, the sampling distribution of the means will be normally distributed, REGARDLESS of the distribution of the account balances themselves. [NO, ANSWER]