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 almost always in control, 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. What cost variance investigation policy should be used? That is, how large a cost variance should trigger an investigation? Using this new policy, what is the probability that an out- of- control cost variance for Process B will be investigated?