Probability Concepts. Narcissism Records, Inc., has just completed an agreement to re-release a recording of The...

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Probability Concepts. Narcissism Records, Inc., has just completed an agreement to re-release a recording of "The Boss's Greatest Hits." The Boss had a number of hits on the rock-and-roll charts during the early 1980s. Preliminary market research indicates two feasible marketing strategies: (1) concentration on developing general consumer acceptance by advertising on late-night television or (2) concentration on developing distributor acceptance through intensive sales calls by company representatives. Estimates for sales under each alternative plan and payoff matrices according to an assessment of the likelihood of product acceptance under each plan are as follows: Strategy 1 Consumer Television Promotion Strategy 2 Distributor-Oriented Promotion Outcome Outcome Probability (Sales) ($) Probability (Sales) ($) 0.32 250,000 0.125 250,000 0.36 1,000,000 0.750 750,000 0.32 1,750,000 0.125 1,250,000 A. Assuming that the company has a 50 percent profit margin on sales, calculate the expected profits for each plan. B. Construct a simple bar graph of the possible profit outcomes for each plan. Which plan appears to be riskier? C. Calculate the standard deviation and coefficient of variation of the profit distribution associated with each plan. D. Assume that the management of Narcissism has a utility function like the one illustrated in the following figure. Which marketing strategy is best? Relation Between Total Utility and Profit for Narcissism Records, Inc. Utility of Profits (Utils) 16 I Total Utility 14 14.5 14 13.5 13 12 12 10 10 8. 7.5 SO $125 $250 $375 $500 $625 $750 $875 $1,000 Total Profits ($000) 4. 2. Probability Concepts. Narcissism Records, Inc., has just completed an agreement to re-release a recording of "The Boss's Greatest Hits." The Boss had a number of hits on the rock-and-roll charts during the early 1980s. Preliminary market research indicates two feasible marketing strategies: (1) concentration on developing general consumer acceptance by advertising on late-night television or (2) concentration on developing distributor acceptance through intensive sales calls by company representatives. Estimates for sales under each alternative plan and payoff matrices according to an assessment of the likelihood of product acceptance under each plan are as follows: Strategy 1 Consumer Television Promotion Strategy 2 Distributor-Oriented Promotion Outcome Outcome Probability (Sales) ($) Probability (Sales) ($) 0.32 250,000 0.125 250,000 0.36 1,000,000 0.750 750,000 0.32 1,750,000 0.125 1,250,000 A. Assuming that the company has a 50 percent profit margin on sales, calculate the expected profits for each plan. B. Construct a simple bar graph of the possible profit outcomes for each plan. Which plan appears to be riskier? C. Calculate the standard deviation and coefficient of variation of the profit distribution associated with each plan. D. Assume that the management of Narcissism has a utility function like the one illustrated in the following figure. Which marketing strategy is best? Relation Between Total Utility and Profit for Narcissism Records, Inc. Utility of Profits (Utils) 16 I Total Utility 14 14.5 14 13.5 13 12 12 10 10 8. 7.5 SO $125 $250 $375 $500 $625 $750 $875 $1,000 Total Profits ($000) 4. 2.