The First Chicago Bank is reviewing its service charges and interest-paying policies on checking accounts. The daily balance of a checking account is defined to be the balance in the checking account at 2:00pm. The bank has found that for all personal checking accounts the mean of all the daily balances is $800 and the standard deviation is $150.
In addition, the distribution of personal checking account daily balances can be approximated very well with a normal model.
Question 1) What percentage of the bank's customers carry daily balances between $700 and $1,000?
Question 2)The bank is considering paying interest to customers carrying daily checking account balances in excess of a certain amount. If the bank does not want to pay interest to more than 6% of its checking account customers, what is the minimum daily balance on which it should be willing to pay interest?