Because of the relatively high interest rates, most consumers attempt to pay off
ID: 3367110 • Letter: B
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 $27 and a standard deviation of $7.
a. What proportion of the bank’s Visa cardholders pay more than $30 in interest?
b. What proportion of the bank’s Visa cardholders pay more than $40 in interest?
c. What proportion of the bank’s Visa cardholders pay less than $15 in interest?
d. What interest payment is exceeded by only 20% of the bank’s Visa cardholders?
Explanation / Answer
a) P(X > 30)
= P(z > (30 - 27)/7)
= P(z > 0.43)
= 0.3341
b) P(X > 40)
= P(z > (40 - 27)/7)
= P(z > 1.86)
= 0.0316
c) P(X < 15)
= P(z < (15 - 27)/7)
= P(z < -1.71)
= 0.0432
d) z score for 20% area to its right = 0.84
Hence,
Interest payment = 27 + 0.84*7 = 32.88