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 30 dollars and a standard deviation of 9 dollars.

A. What proportion of the bank's Visa cardholders pay more than 34 dollars in interest?

B. What proportion of the bank's Visa cardholders pay more than 39 dollars in interest?

C. What proportion of the bank's Visa cardholders pay less than 21 dollars in interest?

D. What interest payment is exceeded by only 19% of the bank's Visa cardholders?

Answer 1

Given, mean X = 30 and SD = 9.

Formula for Z = (K-X)/SD

1. a) For k = 34, the z-value z = (34 - 30) / 9 = 0.444
   
   Hence P(x > 34) = P(z > 0.444) = [Total area] - [area to the left of 0.444] = 1 - 0.67 = 0.33 = 33%
   
   b) For x = 39, z = (39 - 30) / 9 = 1
   
   Hence P(x > 39) = P(z > 1) = [total area] - [area to the left of 1] = 1 - 0.8413 = 0.1587 = 15.87%

c) For x = 21 , z = (21 - 30) / 9 = -1  

Hence P ( x < 21) = P( z < -1) = [area to the left of z = -1] = 0.1587 = 15.87%

d) Given interest percent = 19%

P(z>x) = 0.19

From z table,

  

Hence interest payment of 37.92 dollars is exceeded only by 19% of cardholders