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Based on this information the prior probabilities

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Unformatted text preview: ager for the NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) the shipment (lot) of incoming material. The historical data indicates that there is 30% chance that the lot is poor quality (S 1), 50% chance that the lot is fair quality (S2), and 20% chance that the lot is good quality (S3). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars. What alternative action should be selected according to maximin criterion? Choose alternative 3, and reject the lot. Max (20, 15, 30) = 30, therefore choose alternative 3 and reject the shipment. AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 1 Topic: Decision Theory 1-1951 Chapter 01 - An Introduction to Business Statistics 82. The quality control manager for the NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) the shipment (lot) of incoming material. The historical data indicates that there is 30% chance that the lot is poor quality (S 1), 50% chance that the lot is fair quality (S2), and 20% chance that the lot is good quality (S3). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars. What alternative action should be selected according to expected monetary value criterion? Choose alternative 2, and further analyze the lot. (EMV)1 = (.3)(20) + (.5)(30) + (.2)(90) = 39 (EMV)2 = (.3)(60) + (.5)(70) + (.2)(15) = 56 (EMV)3 = (.3)(80) + (.5)(50) + (.2)(30) = 55 Max (39, 56, 55) = 56 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 1 Topic: Decision Theory 1-1952 Chapter 01 - An Introduction to Business Statistics 83. The quality control manager for the NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) the shipment (lot) of incoming material. The historical data indicates that there is 30% chance that the lot is poor quality (S 1), 50% chance that the lot is fair quality (S2), and 20% chance that the lot is good quality (S3). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars. What is the maximum amount that the quality control manager would be willing to pay for perfect information? EVPI = 21 Expected payoff under certainty = (.3)(80) + (.5)(70) + (.2)(90) = 77 (EMV)1 = (.3)(20) + (.5)(30) + (.2)(90) = 39 (EMV)2 = (.3)(60) + (.5)(70) + (.2)(15) = 56 (EMV)3 = (.3)(80) + (.5)(50) + (.2)(30) = 55 Max (39, 56, 55) = 56 EVPI = 77 - 56 = 21 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 1 Topic: Decision Theory 1-1953 Chapter 01 - An Introduction to Business Statistics 84. The quality control manager for the NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) the shipment (lot) of incoming material. The historical data indicates that there is 30% chance that the lot is poor quality (S 1), 50% chance that the lot is fair quality (S2), and 20% chance that the lot is good quality (S3). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars. 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 the items are defective. The quality control manager inspects one unit from a recent shipment. After inspecting it he determines that the unit is not defective. Based on this additional information, determine the revised (posterior) probabilities for each of the three states of nature. .24, .52, .24 Let: D = Defective ND = Not defective AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 2 Topic: Posterior Analysis 1-1954 Chapter 01 - An Introduction to Business Statistics 85. The quality control manager for the NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) the shipment (lot) of incoming material. The historical data indicates that there is 30% chance that the lot is poor quality (S 1), 50% chance that the lot is fair quality (S2), and 20% chance that the lot is good quality (S3). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars. 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 the 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. .48, .44, and .08 Let: D = Defective ND = Not defective AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 2 Topic: Posterior Analysis 1-1955 Chapter 01 - An...
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This document was uploaded on 01/20/2014.

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