In the book Advanced Managerial Accounting, Robert P.Magee discusses monitoring cost variances. A cost varianceis the difference between a budgeted cost and an actual cost. Mageedescribes the following situation:
Michael Bitner has responsibility for control of twomanufacturing processes. Every week he receives a cost variancereport for each of the two processes, broken down by labor costs,materials costs, and so on. One of the two processes, which we'llcall process A , involves a stable, easily controlledproduction process with a little fluctuation in variances. ProcessB involves more random events: the equipment is moresensitive and prone to breakdown, the raw material prices fluctuatemore, and so on.
     \"It seems like I'm spending moreof my time with process B than with process A,\"says Michael Bitner. \"Yet I know that the probability of aninefficiency developing and the expected costs of inefficienciesare the same for the two processes. It's just the magnitude ofrandom fluctuations that differs between the two, as you can see inthe information below.\"
     \"At present, I investigatevariances if they exceed $2,789, regardless of whether it wasprocess A or B. I suspect that such a policy isnot the most efficient. I should probably set a higher limit forprocess B.\"
The means and standard deviations of the cost variances ofprocesses A and B, when these processes are incontrol, are as follows: (Round your z value to 2 decimalplaces and final answers to 4 decimal places.):
| Process A | Process B |
| Mean cost variance (in control) | $ 5 | $ 0 |
| Standard deviation of cost variance (in control) | $5,105 | $10,342 |
|
Furthermore, the means and standard deviations of the costvariances of processes A and B, when theseprocesses are out of control, are as follows:
| Process A | Process B |
| Mean cost variance (out of control) | $7,048 | $ 6,130 |
| Standard deviation of cost variance (out of control) | $5,105 | $10,342 |
|
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(a) Recall that the current policy is toinvestigate a cost variance if it exceeds $2,789 for eitherprocess. Assume that cost variances are normally distributed andthat both Process A and Process B cost variancesare in control. Find the probability that a cost variance forProcess A will be investigated. Find the probability thata cost variance for Process B will be investigated. Whichin-control process will be investigated more often.
Process A = ___
Process B = ___
_(A or B)__ Process is investigated more often
(b) Assume that cost variances are normallydistributed and that both Process A and Process Bcost variances are out of control. Find the probability that a costvariance for Process A will be investigated. Find theprobability that a cost variance for Process B will beinvestigated. Which out-of-control process will be investigatedmore often.
Process A = ___
Process B = ___
_(A or B)__ Process is investigated more often
(c) If both Processes A and Bare almost always in control, which process will be investigatedmore often.
_(A or B)__ Process is investigated more often
(d) Suppose that we wish to reduce theprobability that Process B will be investigated (when itis in control) to .2912. What cost variance investigation policyshould be used? That is, how large a cost variance should triggeran investigation? Using this new policy, what is the probabilitythat an out-of-control cost variance for Process B will beinvestigated?
Process A = ___
Process B = ___
