The quality control manager for NKA Inc. must decide whether to accept, further analyze or reject the shipment (lot) of incoming material. The historical data indicates that there is 30% chance that the lot is poor quality, 50% chance that the lot is fair quality and 20% chance that the lot is good quality. Assume the following payoff table is available. The values in the payoff table are in thousands of dollars.

States of Nature

Determine the expected monetary value for each alternative and determine the best course of action for this problem.

What is the maximum amount that the quality control manager would be willing to pay for perfect information?

Based on historical data, if the lot is poor quality, 40% of the items are defective. If the lot is fair quality 22% of the items are defective. If the lot is good quality, 10% of items are defective. The quality control manager inspects one unit from a recent shipment. After inspecting it he determines that the unit is defective. Based on this additional information, determine the revised (posterior) probabilities for each of the three states of nature.

After inspecting it, he determines that the unit is defective. If the inspected item is defective, determine which alternative action the quality control manager should choose [use the revised (posterior) probabilities calculated in question 11, recalculate the expected monetary value for each alternative].

Decision	Poor	Fair	Good
Accept	20	30	90
Further Analyze	60	70	15
Reject	80	50	30