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 30 dollars and a standard deviation of 7 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 39 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?

Answer 1

Let X be the amount of interest paid by Bank's visa cardholders

X~ N( 30, 7)

a) P( X> 33) = P( > )

= P( z > 0.43)

= 1- P(z < 0.43)

= 1- 0.66640

=0.3336

b) P( X > 39) = P( > )

= P( z > 0.43)

= 1- P(z < 1.28)

= 1- 0.89973

=0.10027
c) P( X < 18) = P( < )

= P( z < -1.71)

= 1- P( z < 1.71)

= 1- 0.95637

= 0.04363

d) Interest payment is exceeded by only 21% of the bank's Visa cardholders

That means that we need to find the 21st percentile

P( Z <z ) =0.21

P( Z < -0.806 ) = 0.21

z = -0.806

   = -0.806

   = -0.806

X = 30 - (0.806 * 7)

X = $24.358