Nikhil is a sales representative. He is primarily responsible for selling water purifiers by visiting

customer offices.

In each visit, the probability of securing a purchase order is 0.8, independently of the other visits.

When he secures a purchase order, he offers an extended warranty, which the customer orders with probability 0.6. (Unless there is a purchase, there is no question of extended warranty.)

a) How many visits is Nikhil expected to make, to secure his first purchase order?

b) How many visits is Nikhil expected to make, to secure his first extended warranty order?

For the remaining problems, assume that Nikhil is going to make exactly 5 visits.

c) What is the probability that Nikhil secures 3 purchase orders in the 5 visits, and all are with extended warranty orders?

d) What is the probability that Nikhil gets 3 extended warranty orders in the 5 visits?

e) Given Nikhil gets at least 3 purchase orders in the 5 visits, what is the conditional probability that he gets no extended warranty order in any of these?

Problem 2

In the book Advanced Managerial Accounting, Robert P. Magee discusses monitoring cost variances. A cost variance is the difference between a budgeted cost and an actual cost. Magee considers weekly monitoring of the cost variances of two manufacturing processes, Process A and Process B. One individual monitors both processes and each week receives a weekly cost variance report for each process. The individual has decided to investigate the weekly cost variance for a particular process (to determine whether or not the process is out of control) when its weekly cost variance is too high. To this end, a weekly cost variance will be investigated if it exceeds $2,500.

a) When Process A is in control, its potential weekly cost variances are normally distributed with a mean of $0 and a standard deviation of $5,000. When Process B is in control, its potential weekly cost variances are normally distributed with a mean of $0 and a standard deviation of $10,000. For each process, find the probability that a weekly cost variance will be investigated (that is, will exceed $2,500) even though the process is in control. Which in-control process will be investigated more often?

b) When Process A is out of control, its potential weekly cost variances are normally distributed with a mean of $7,500 and a standard deviation of $5,000. When Process B is out of control, its potential weekly cost variances are normally distributed with a mean of $7,500 and a standard deviation of $10,000. For each process, find the probability that a weekly cost variance will be investigated (that is, will exceed $2,500) when the process is out of control. Which out-of-control process will be investigated more often?

c) If both Processes A and B are in control 95% of the times and out of control 5% of the times, which

process will be investigated more often?

d) Suppose that we wish to reduce the probability that Process B will be investigated (when it is in control) to .3085.

I. What cost variance investigation policy should be used? That is, how large a cost variance should trigger an investigation?

II. Using this new policy, what is the probability that an out-of-control cost variance for Process B will be investigated?