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 $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?

Answer 1

Answer:

The percentage of the bank's customers carry daily balances between $700 and $1,000 is 65.7%.

The minimum daily balance on which it should be willing to pay interest is $1,198.

Step-by-step explanation:

We have a normal distribution with mean = $800 and standard deviation = $150.

a) We can calculate this value with the standard normal distribution, calculating the z-value for $700 and $1,000.

$z_1=\frac{x-\mu}{\sigma} =\frac{700-800}{150}= \frac{-100}{150} =-0.67\\\\\\z_2=\frac{1,000-800}{150}=\frac{200}{150}=1.33\\\\\\P(700$

The percentage of the bank's customers carry daily balances between $700 and $1,000 is 65.7%.

b) We must calculate from what amount only 6% of the accounts remain.

This is done by solving:

$P(z>x)=0.06$

This happens for a z-value of z=2.652.

This corresponds to a amount of $1,198.

$x=\mu+z*\sigma=800+2.652*150=800+398=1,198$

The minimum daily balance on which it should be willing to pay interest is $1,198.