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 8 dollars.
A. What proportion of the bank's Visa cardholders pay more than 32 dollars in interest?

Proportion =

B. What proportion of the bank's Visa cardholders pay more than 40 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 19% of the bank's Visa cardholders?

Answer 1

Answer:

Step-by-step explanation:

Let X be average interest paid monthly by a bank's Visa cardholders

Given that X is N(28, 8)

In the following to find out probability we convert X to z score and use std normal distribution table

Z = $\frac{x-28}{8}$

Probability being less than 1 is here equal to the proportion also.

A) P(X>32) = P(Z>0.5)=0.5-0.1915=0.3085

B) P(X>40) = P(Z>1)=0.5-0.3413=0.1687

C) P(X<19) = P(Z<-1.125)=0.5-0.0438=0.4562

D) We have to find 19th percentile here

Z =-0.88

$X=28-0.88(8)\\=20.96$