Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

statistics The finance director of a hardware wholesaler has asked the accountan

ID: 3179837 • Letter: S

Question

statistics The finance director of a hardware wholesaler has asked the accountant to ring each customer five days before their account payment is due, as a means of reducing the number of payments. As a result of time constraints, however, only 60% of customers receive such a call from the accountant. Of the customers called, 90% pay on time, while 50% of those not called pay on time. The company has just received a payment on time from a customer. What is the probability that the accountant called the custom?

Explanation / Answer

A - probability payment is received

X - probability that the accountant called customer = 0.6

XC - probability that the accountant did not call the customer = 0.4

A/X - proabability that the customer paid on time given the accountant called the customer = 0.9

A/Xc - proabability that the customer paid on time given the accountant didn't call the customer = 0.5

X/A - probability that accountant called customer given that the payment is received

As per Bayes' theorem,

P (X/A) = P(A/X). P(X) / [P(A/X). P(X) + P(A/XC ). P(XC) ]

= 0.9 * 0.6/ [0.9*0.6 + 0.5* 0.4 ]

=0.54/ (0.54+0.20] = 0.54/0.74 = 0.7297