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# The quality control manager for the nka inc must

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Unformatted text preview: Introduction to Business Statistics 86. 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. If the inspected item is defective, determine which alternative action the quality control manager should choose. (EMV)3 = 62.8, reject the shipment. Let: D = Defective ND = Not defective (EMV)1 = (.48) (20) + (.44) (30) + (.08) (90) = 30 (EMV)2 = (.48) (60) + (.44) (70) + (.08) (15) = 60.8 (EMV)3 = (.48) (80) + (.44) (50) + (08) (30) = 62.8 Max (30, 60.8, 62.8) = 62.8, reject the shipment. AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 2 Topic: Posterior Analysis 1-1956 Chapter 01 - An Introduction to Business Statistics 87. 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. If the inspected item is defective, determine which alternative action the quality control manager should choose. Choose alternative 2 and further analyze the shipment. Let: D = Defective ND = Not defective (EMV)1 = (.24) (20) + (.52) (30) + (.24) (90) = 42 (EMV)2 = (.24) (60) + (.52) (70) + (.24) (15) = 54.4 (EMV)3 = (.24) (80) + (.52) (50) + (.24) (30) = 52.4 Max (42, 54.4, 52.4) = 54.4, choose alternative 2 and further analyze the shipment. AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 2 Topic: Posterior Analysis 1-1957 Chapter 01 - An Introduction to Business Statistics 88. A decision maker has prepared the following decision tree. There are two main decision alternatives (A and B). The probabilities for the states of nature are as follows: P(H) = .3, P(M) = .5, P(L) = .2, P(S) = .25, P(P) = .75. Calculate the highest expected profit for the decision maker and determine which of the two alternatives he/she should select. 1-1958 Chapter 01 - An Introduction to Business Statistics Choose option A, EMGA = 61.3 EMG1 = (.25) (60) + (.75) (88) = 81 EMG2 = (.25) (20) + (.75) (48) = 41 EMG3 = (.3) (81) + (.5) (58) + (.20) (40) = 61.3 EMG4 = (.3) (80) + (.5) (55) + (.20) (41) = 59.7 We choose option A because EMGA = 61.3 > EMGB = 59.7 AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 1 Topic: Decision Theory 1-1959 Chapter 01 - An Introduction to Business Statistics 89. A company wants to add a new product to its existing line of products. There are two similar candidate products A and B. The demand for the new product could be high, medium, or low with probabilities of .25, .5, and .25 respectively. The demand and the corresponding profit for each product is: Which product should the company select based on the expected monetary value criterion? Product A has a higher expected monetary value A Expected monetary value = .25(40000) + .5(30000) + .25(20000) = 30,000 B Expected monetary value = .25(70000) + .5(20000) + .25(0) = 27,500 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 1 Topic: Decision Theory 1-1960 Chapter 01 - An Introduction to Business Statistics 90. An investor is looking at three possible investments - growth stock, blue chip stock, or municipal bonds. The investment performance will vary depending on the investment market condition of Bull (market rising), flat, or Bear (market falling). The investment return for each investment for the corresponding market conditions is given below: Which investment would the investor select if the maximin criterion is used? Bonds Worst investment performance Growth Stock-6 Blue Chip 0 Bonds 4 Bonds have the maximum worst possible payoff. AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 1 Topic: Decision Theory 1-1961 Chapter 01 - An Introduction to Business Statistics 91. An investor is looking at three possible investments - growth stock, blue chip stock, or municipal bonds. The investment performance will vary depending on the investment market condition of Bull (market rising), flat, or Bear (market falling). The investment return for each investment for the corresponding market conditions is given below: Which investment would the investor select if the maximax criterion is used? Growth stock Best investment performance Growth Stock 20 Blue Chip 9 Bonds 4 Growth Stock has the maximum possible payoff. AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 1 Topic: Decision Theory 1-1962...
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