An engineering company's plant maintenance budget for the month of May is showing an adverse cost variance of Rs 1,200 on a total budget of Rs 20,000. The factory manager is uncertain whether it would be worthwhile investigating the cost variance and taking any corrective action since he estimates this will cost Rs 1,000. Further, he estimates that given the usual variation on his maintenance costs, he would only have a 50% chance in any case of being in the range of Rs 19,500 - Rs 20,500.

Higher than planned maintenance costs could be due to engineering failures more complex than expected.

These would be rectified after investigation. The manager estimates that consequential losses of not investigating such a situation could amount to Rs 4,000.

(a) Calculate the standard deviation of the estimated maintenance costs;

(b) set out the pay-off table for action on the decision as to investigation of variance;

(c) state the decision rule and the probability that the process is out of control which would lead to a decision to investigate;

(d) advise the manager as to whether he should investigate the causes of the variances in May budget.

(Assume that the variances in the maintenance budget follow a normal probability pattern).