Question

Wildcat Electronics sells audio and video equipment. Its billing division has information on the age of its accounts receivables. The data collected indicate that the age of the accounts follows a normal distribution with a mean of 12 days and a standard deviation of 9 days.

(A1) The billing division is sending reminder emails to its oldest 25% of accounts. How many days old should an account at least be to receive a reminder?

(A2) Wildcat Electronics charges a late fee of $50 when an account is 30 days or older. What percentage of the accounts will receive this late fee?

(A3) Wildcat Electronics wants to give a discount to those accounts that pay their balance within 7 days. What percentage of the accounts will receive the discount?

Answer 1

1). we have

mean u=12 days

std deviation σ =9 days

a. oldest 25% means top 25%

so

P(X>x)=0.25 or

P(X<x)=0.75 or

P(Z<z)=0.75

z=0.68

so

0.68=(x-12)/9 or

x=18.12 days old,so it should be 18.12 days old to get a reminder.

b.

P(X>30)=P(Z>(30-12)/9)

=P(Z>2)=0.0228

so, 2.28% accounts will be charged with a fine of $50.

c.

within 7 days means

P(X<7)=P(Z<(7-12)/9)

=P(Z<-0.56)=0.2877

so, 28.77% accounts will be given a discount.

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