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 9 dollars.

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

Proportion =

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

Proportion =

Answer 1

Solution :

Given ,

mean = $\mu$ = $26

standard deviation = $\sigma$ =$ 9

(a)P(x >$28 ) = 1 - P(x< 28)

= 1 - P[(x -$\mu$) / $\sigma$ < (28-26) / 9]

= 1 - P(z < 0.22)

Using z table

= 1 - 0.5871

= 0.4129

Proportion=0.4129

(b)

P(x >$38 ) = 1 - P(x< 38)

= 1 - P[(x -$\mu$) / $\sigma$ < (38-26) /9 ]

= 1 - P(z < 1.33)

Using z table

= 1 - 0.9082

= 0.0918

Proportion=0.0918