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 6 dollars. 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 38 dollars in interest Proportion- C. What proportion of the bank's Visa cardholders pay less than 18 dollars in interest? Proportion D. What interest payment is exceeded by only 21 % of the bank's Visa cardholders? Interest Payment-

Answer 1

X : Amount of interest paid monthly by bank's Visa card holdres.

X ~ N ( 29, 6²)

by central limit theorem

Z = ( X -29)/6 ~ N(0,1)

a) Propertion of the bank's Visa cardholders pay more than $33 in interest

=P ( X > 33)

= P (  ( X -29)/6 > (33-29)/6)

=P(Z > 0.6667)

From normal probability table

P(Z > 0.6667) = 0.2525

Propertion = 25.25%

b ) Propertion of the bank's Visa cardholders pay more than $38 in interest

=P ( X > 38)

= P (  ( X -29)/6 > (38-29)/6)

=P(Z > 1.5)

From normal probability table

P(Z >1.5) = 0.0668

Propertion = 6.68%

c) Propertion of the bank's Visa cardholders pay less than $18 in interest

=P ( X<18)

= P (  ( X -29)/6 < (18-29)/6)

=P(Z< -1.8333)

From normal probability table

P(Z <-1.8333) = 0.0333

Propertion = 3.33%

d) P(X >a) = 0.21

P( (X-a)/6 > (a-29)/6 ) = 0.21

P(Z > (a-29)/6 ) =0.21 ------------(I)

From normal probability table

P(Z > 0.806) = 0.21 --------------(II)

From (I) and (II)

(a-29)/6 = 0.806

a = 33.836

Interest payment = $33.836