A bank has kept records of the balances of its customers’ account, which is normally distributed with the average daily balance of $500 and standard deviation of $50. (a) For a sample of 22 randomly...

A bank has kept records of the balances of its customers’ account, which is normally distributed with the average daily balance of $500 and standard deviation of $50.

 (a) For a sample of 22 randomly selected accounts, what is the distribution of the sample mean? What are the mean, variance and standard deviation of this distribution?

(b) What is the probability that the sample mean of 16 randomly selected accounts will be more than $400?

 (c) What is the probability that the sample mean of 16 randomly selected accounts will be less than $350?

(d) What is the probability that the sample mean of 36 randomly selected accounts will be between $350 and $400?

(e) If the population of the balances of customers’ accounts is not normally distributed, which, if any, of the questions above can you answer? Justify your answer.