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 $700 and the standard deviation is $200.

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)

dollars

Answer 1

Solution :

Given that ,

mean = = 700

standard deviation = = 200

1)

P(700 < x < 1000) = P((700 - 700)/ 200) < (x - ) /  < (1000 - 700) / 200) )

= P(0 < z < 1.5)

= P(z < 1.5) - P(z < 0)

= 0.9332 - 0.5

= 0.4332

Answer = 43.32%

2)

P(Z > z) = 5%

1 - P(Z < z) = 0.05

P(Z < z) = 1 - 0.05 = 0.95

P(Z < 1.645) = 0.95

z = 1.645

Using z-score formula,

x = z * +

x = 1.645 * 200 + 700 = 1029

minimum daily balance = $1029