Because of the relatively high interest rates, most consumers attempt to pay off
ID: 2922426 • 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 dollars and a standard deviation of 7 dollars.
A. What proportion of the bank's Visa cardholders pay more than 30 dollars in interest?
Proportion =
B. What proportion of the bank's Visa cardholders pay more than 37 dollars in interest?
Proportion =
C. What proportion of the bank's Visa cardholders pay less than 17 dollars in interest?
Proportion =
D. What interest payment is exceeded by only 19% of the bank's Visa cardholders?
Interest Payment =
Explanation / Answer
Mean is 27 and s is 7. z is calculated as (x-mean)/s
a) P(x>30) =P(z>(30-27)/7)=P(z>0.43) or 1-P(z<0.43)
from normal distribution table we get 1-0.6664=0.3336
b) P(x>37)=P(z>(37-27)/7)=P(z>1.43) or 1-P(z<1.43)
from normal distribution table we get 1-0.9236=0.0764
c) P(x<17)=P(z<(17-27)/7)=P(z<-1.43)=1-P(z<1.43) =0.0764
d) P(x<X)=0.19
thus we need to find z for 0.19 which can be found by negating the value of 1-0.19=0.81
thus, we get z=-0.7910
thus, (x-27)/7=-0.7910
thus x=-0.7910*7+27 =21.463