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 26 dollars and a standard deviation of 8 dollars.

A. What proportion of the bank's Visa cardholders pay more than 28 dollars in interest?

B. What proportion of the bank's Visa cardholders pay more than 38 dollars in interest?

C. What proportion of the bank's Visa cardholders pay less than 17 dollars in interest?

D. What interest payment is exceeded by only 22% of the bank's Visa cardholders?

Answer 1

Let ,

A.

; From standard normal distribution table

Therefore , the proportion of the bank's Visa cardholders pay more than 28 dollars in interest is 0.4013

B. Now ,

; From standard normal distribution table

Therefore , the proportion of the bank's Visa cardholders pay more than 38 dollars in interest is 0.0668

C. Now ,

; From standard normal distribution table

Therefore , the proportion of the bank's Visa cardholders pay less than 17 dollars in interest is 0.1292

D. We have ,

................(I)

  From standard normal distribution table , ................(II)

From (I) and (II) , we get ,

Therefore , the interest payment is exceeded by only 22% of the bank's Visa cardholders is 32.16