Because of the relatively high interest rates, most consumers attempt to pay off

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 29 dollars and a standard deviation of 8 dollars.Please use z-scores with at least 3 decimal places.

A. What proportion of the bank's Visa cardholders pay more than 33 dollars in interest? Proportion =

B. What proportion of the bank's Visa cardholders pay more than 39 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 20% of the bank's Visa cardholders? Interest Payment =

Explanation / Answer

Solution :

Given that mean ? = 29 and a standard deviation ? = 8

A. P(x > 33) = P((x - ?)/? > (33 - 29)/8)

= P(Z > 0.500)

= 0.3085

B. P(x > 39) = P((x - ?)/? > (39 - 29)/8)

= P(Z > 1.250)

= 0.1056

C. P(x < 19) = P((x - ?)/? < (19 - 29)/8)

= P(Z < -1.250)

= 0.1056

D. P = 0.2 then Z-score = 0.8416

X = ? + Z*?

= 29 + 0.8416*8

= 35.7328

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