Question

Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank's Visa cardholders reveals that the amount is normally distributed with a mean of 28 dollars and a standard deviation of 9 dollars.

A. What proportion of the bank's Visa cardholders pay more than 30 dollars in interest?

Proportion =

B. What proportion of the bank's Visa cardholders pay more than 37 dollars in interest?

Proportion =

C. What proportion of the bank's Visa cardholders pay less than 19 dollars in interest?

Proportion =

D. What interest payment is exceeded by only 21% of the bank's Visa cardholders?

Interest Payment =

Answer 1

Solution: We are given:

A. What proportion of the bank's Visa cardholders pay more than 30 dollars in interest?

Answer: Proportion = 0.4129

Proof:

Let x be the amount payed by bank's Visa cardholder.

We have to find

  

Now we need to find .

Using the standard normal table we have:

Therefore the proportion of the bank's Visa cardholders who pay more than 30 dollars in interest is

B. What proportion of the bank's Visa cardholders pay more than 37 dollars in interest?

Answer: Proportion =0.1587

Proof:

Let x be the amount payed by bank's Visa cardholder.

We have to find

  

Now we need to find .

Using the standard normal table we have:

Therefore the proportion of the bank's Visa cardholders who pay more than 37 dollars in interest is

C. What proportion of the bank's Visa cardholders pay less than 19 dollars in interest?

Answer: Proportion = 0.1587

Proof:

Let x be the amount payed by bank's Visa cardholder.

We have to find

  

Now we need to find .

Using the standard normal table we have:

Therefore the proportion of the bank's Visa cardholders who pay less than 19 dollars in interest is

D. What interest payment is exceeded by only 21% of the bank's Visa cardholders?

Answer: Interest Payment = 35.2576

Proof: We need to first find the  z-value with a right-tail of 0.21.

Therefore invNorm(0.79) = 0.8064

Now let's find the interest payment: