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.

$z_1=\frac{x-\mu}{\sigma} =\frac{700-800}{150}= \frac{-100}{150} =-0.67\\\\\\z_2=\frac{1,000-800}{150}=\frac{200}{150}=1.33\\\\\\P(700<x<1000)=P(-0.67<z<1.33)\\\\P( 700<x<1000)=P(z<1.33)-P(z<-0.67)\\\\P(700<x<1000)=0.90824-0.25143=0.657$

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.

Answer 2

The percentage of the bank's customers carrying daily balances between $700 and $1,000 is 6.57% and the minimum daily balance on which it should be willing to pay interest is $1198.

Given :

• 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 2:00 pm.
• 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.

1) First calculated the value of z in order to determine the percentage of the bank's customers carrying daily balances between $700 and $1,000.

$\rm z_1=\dfrac{700-800}{150} = -0.67$

$\rm z_2=\dfrac{1000-800}{150}=1.33$

P(700< x <1000) = P(-0.67 < z < 1.33)

                           = P(z < 1.33) - P(z > -0.67)

                           = 0.90824 - 0.25143

                           = 0.657

                           = 6.57%

2) The value of x is given by the formula:

$\rm x = \mu+z\times \sigma$

$x = 800+2.652\times 150 = 1198$

For more information, refer to the link given below:

https://brainly.com/question/11897796