In the bookAdvanced Managerial Accounting, Robert P. Magee discusses monitoring cost variances. Acost varianceis the difference between a budgeted cost and an actual cost. Magee describes the following situation:

Michael Bitner has responsibility for control of two manufacturing processes. Every week he receives a cost variance report for each of the two processes, broken down by labor costs, materials costs, and so on. One of the two processes, which we'll call processA, involves a stable, easily controlled production process with a little fluctuation in variances. ProcessBinvolves more random events: the equipment is more sensitive and prone to breakdown, the raw material prices fluctuate more, and so on.

"It seems like I'm spending more of my time with processBthan with processA," says Michael Bitner. "Yet I know that the probability of an inefficiency developing and the expected costs of inefficiencies are the same for the two processes. It's just the magnitude of random fluctuations that differs between the two, as you can see in the information below."

"At present, I investigate variances if they exceed $2,713, regardless of whether it was processAorB. I suspect that such a policy is not the most efficient. I should probably set a higher limit for processB."

The means and standard deviations of the cost variances of processesAandB, when these processes are in control, are as follows:(Round your z value to2 decimal placesand final answers to 4 decimal places.):

ProcessA

Mean cost variance (in control)$ 2

Standard deviation of cost variance (in control)$4,849

ProcessB

Mean cost variance (in control)$ 5

Standard deviation of cost variance (in control)$9,853

Furthermore, the means and standard deviations of the cost variances of processesAandB, when these processes are out of control, are as follows:

ProcessA

Mean cost variance (out of control)$6,680

Standard deviation of cost variance (out of control)$4,849

ProcessB

Mean cost variance (out of control)$ 6,063

Standard deviation of cost variance (out of control)$9,853

(a)Recall that the current policy is to investigate a cost variance if it exceeds $2,713 for either process. Assume that cost variances are normally distributed and that both ProcessAand ProcessBcost variances are in control. Find the probability that a cost variance for ProcessAwill be investigated. Find the probability that a cost variance for ProcessBwill be investigated. Which in-control process will be investigated more often.

Process A=?

Process B=?

(b)Assume that cost variances are normally distributed and that both ProcessAand ProcessBcost variances are out of control. Find the probability that a cost variance for ProcessAwill be investigated. Find the probability that a cost variance for ProcessBwill be investigated. Which out-of-control process will be investigated more often.

Process A=?

Process B=?

(c)If both ProcessesAandBare almost always in control, which process will be investigated more often.

Process A or Process B?

(d)Suppose that we wish to reduce the probability that ProcessBwill be investigated (when it is in control) to .2877. 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 ProcessBwill be investigated?

k =?

P(x> 5,523)=?