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Solution-Tutorial-4

# Solution-Tutorial-4 - AB103 Statistical and Quantitative...

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1 AB103 – Statistical and Quantitative Methods Solutions - Tutorial 4 Chapters 6 Anderson, Sweeney, Williams, and Martin (ASWM) 6.4 (page 326) a. The decision is to choose the best lease option; there are three alternatives. The chance event is the number of miles Amy will drive per year. There are three possible outcomes. b. The payoff table for Amy's problem is shown below. To illustrate how the payoffs were computed, we show how to compute the total cost of the Forno Saab lease assuming Amy drives 15,000 miles per year. Total Cost = (Total Monthly Charges) + (Total Additional Mileage Cost) = 36(\$299) + \$0.15(45,000 - 36,000) = \$10,764 + \$1350 = \$12,114 c. Optimistic Approach: Forno Saab (\$10,764) Conservative Approach: Hopkins Automotive (\$11,700) Opportunity Loss or Regret Table

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2 d. EV (Forno Saab) = 0.5(\$10,764) + 0.4(\$12,114) + 0.1(\$13,464) = \$11,574 EV (Midtown Motors) = 0.5(\$11,160) + 0.4(\$11,160) + 0.1(\$12,960) = \$11,340 EV (Hopkins Automotive) = 0.5(\$11,700) + 0.4(\$11,700) + 0.1(\$11,700) = \$11,700 Best Decision: Midtown Motors e. f. EV (Forno Saab) = 0.3(\$10,764) + 0.4(\$12,114) + 0.3(\$13,464) = \$12,114 EV (Midtown Motors) = 0.3(\$11,160) + 0.4(\$11,160) + 0.3(\$12,960) = \$11,700 EV (Hopkins Automotive) = 0.3(\$11,700) + 0.4(\$11,700) + 0.3(\$11,700) = \$11,700 Best Decision: Midtown Motors or Hopkins Automotive With these probabilities, Amy would be indifferent between the Midtown Motors and Hopkins Automotive leases. However, if the probability of driving 18,000 miles per year goes up any further, the Hopkins Automotive lease will be the best.