Question

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 $900 and the standard deviation is $125.

In addition, the distribution of personal checking account daily balances can be approximated very well with a normal model.

QUESTION: What percentage of the bank's customers carry daily balances between $700 and $1,000?(Use 2 decimal places in your answer. Note that the answer is requested as a percent, that is, a value between 0 and 100).

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 4% of its checking account customers, what is the minimum daily balance on which it should be willing to pay interest?

Answer 1

QUESTION: What percentage of the bank's customers carry daily balances between $700 and $1,000?(Use 2 decimal places in your answer. Note that the answer is requested as a percent, that is, a value between 0 and 100).

µ	900
σ	125
x	700
z = (x - µ)/σ	-1.6
p-value	0.054799
x	1000
z = (x - µ)/σ	0.8
p-value	0.788145
Required probability	73.33%

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 4% of its checking account customers, what is the minimum daily balance on which it should be willing to pay interest?

z	-1.75069
x	681.1642