The Webster National Bank is reviewing its service charge and interest-paying policies on checking accounts. The bank has found that the average daily balance on personal checking accounts is $550, with a standard deviation of
$150. In addition, the average daily balances have been found to be normally distributed (Gaussian).
(a) What percentage of personal checking account customers carry average daily balances in excess of $800?
(b) What percentage of the bank's customers carries average daily balances below of $200?
(c) What percentage of the bank's customers carries average daily balances between $300 and $700?
(d) The bank is considering paying interest to customers carrying average daily balances in excess of a certain amount. If the bank does not want to pay interest to more than 5% of its customers, what is the minimum average daily balance it should be willing to pay interest on?