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36. A manager has developed a table that shows payoffs for a future store. The payoffs depend on the size of the store and the strength of demand (in thousands): Store size Demand High 2.500 4,000 Low Small Large 1,500 500 The manager estimates that the probability of low demand is 0.50, and the probability of high demand is 0.50. The manager could request that a local research firm conduct a survey (cost: 100,000) that could better indicate whether demand will be low or high. In discussion with the research firm, the manager has learned the following about the reliability of surveys conducted

36. A manager has developed a table that shows payoffs for a future store. The payoffs depend on the size of the store and the strength of demand (in thousands): Store size Demand High 2.500 4,000 Low Small Large 1,500 500 The manager estimates that the probability of low demand is 0.50, and the probability of high demand is 0.50. The manager could request that a local research firm conduct a survey (cost: 100,000) that could better indicate whether demand will be low or high. In discussion with the research firm, the manager has learned the following about the reliability of surveys conducted

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 81E
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36. A manager has developed a table that shows payoffs for a future store. The payoffs depend on the size of the store and the strength of demand (in thousands): Store size Demand Low High Small Large 1,500 2,500 500 4,000 The manager estimates that the probability of low demand is 0.50, and the probability of high demand is 0.50. The manager could request that a local research firm conduct a survey (cost: 100,000) that could better indicate whether demand will be low or high. In discussion with the research firm, the manager has learned the following about the reliability of surveys conducted by the firm: Survey showed Actual results was High 0.30 Low Low 0.90 High 0.10 0.70 a. If the manager should decide to use the survey, what would the revised probabilities be for demand, and what probabilities should be used for survey results? b. Construct a tree diagram for this problem c. Would you recommend that the manager use the survey ?
Transcribed Image Text:36. A manager has developed a table that shows payoffs for a future store. The payoffs depend on the size of the store and the strength of demand (in thousands): Store size Demand Low High Small Large 1,500 2,500 500 4,000 The manager estimates that the probability of low demand is 0.50, and the probability of high demand is 0.50. The manager could request that a local research firm conduct a survey (cost: 100,000) that could better indicate whether demand will be low or high. In discussion with the research firm, the manager has learned the following about the reliability of surveys conducted by the firm: Survey showed Actual results was High 0.30 Low Low 0.90 High 0.10 0.70 a. If the manager should decide to use the survey, what would the revised probabilities be for demand, and what probabilities should be used for survey results? b. Construct a tree diagram for this problem c. Would you recommend that the manager use the survey ?
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