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 $750 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?

  % (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 5% of its checking account customers, what is the minimum daily balance on which it should be willing to pay interest? (Round your answer to the nearest dollar)

Answer 1

Solution :

Given that ,

mean = = $ 750

standard deviation = = $ 150

a) P(700 < x < 1000) = P[(700 - 750) / 150) < (x - ) /  < (1000 - 750) / 150) ]

= P(-0.33 < z < 1.67)

= P(z < 1.67) - P(z < -0.33)

Using z table,

= 0.9525 - 0.3707

= 0.5818

the percentage is = 58.18%

b) Using standard normal table,

P(Z < z) = 5%

= P(Z < z) = 0.05  

= P(Z < -1.645) = 0.05

z = -1.645

Using z-score formula,

x = z * +

x = -1.645 * 150 +750

x = 503.25

x = $ 503