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.

What interest payment is exceeded by only 20% of the bank's Visa cardholders?

Interest Payment =

Note: Please show work, it would be really helpful and I wold appreciate it.

Answer 1

Solution:-

Given that,

mean = = 28 dollars

standard deviation = = 9 dollars

Using standard normal table,

P(Z > z) = 20%

= 1 - P(Z < z) = 0.20  

= P(Z < z) = 1 - 0.20

= P(Z < z ) = 0.80

= P(Z < 0.8416 ) = 0.80  

z = 0.8416

Using z-score formula,

x = z * +

x = 0.8416 * 9 + 28

x = 35.57

Interest Payment = 36 dollars