Roger Hunt intends to purchase one of two car dealerships currently for sale in

Question

Roger Hunt intends to purchase one of two car dealerships currently for sale in a certain city. Records obtained from each of the two dealers reveal that their weekly volume of sales, with corresponding probabilities, are as follows. Dahl Motors Cars Sold/Week 5 6 7 8 9 10 11 12 Probability 0.05 0.09 0.14 0.24 0.18 0.14 0.11 0.05 Farthington Auto Sales Cars Sold/Week 5 6 7 8 9 10 Probability 0.08 0.21 0.31 0.24 0.10 0.06 The average profit per car at Dahl Motors is $542, and the average profit per car at Farthington Auto Sales is $653. (a) Find the average number of cars sold each week at each dealership. Dahl cars Farthington cars (b) If Roger's objective is to purchase the dealership that generates the higher weekly profit, which dealership should he purchase? (Compare the expected weekly profit for each dealership.) The expected weekly profit from Dahl Motors is $ . The expected weekly profit from Farthington Auto Sales is $ . Therefore, Roger should purchase .

Explanation / Answer

(A)

Average number of cars sold every week at Dahl cars = 5*0.05 + 6*0.09 + 7*0.14 + 8*0.24 + 9*0.18 + 10*0.14 + 11*0.11 + 12*0.05 = 8.52

Average number of cars sold every week at Farthington cars = 5*0.08 + 6*0.21 + 7*0.31 + 8*0.24 + 9*0.10 + 10*0.06 = 7.25

(b) Average profit of Dahl = 8.52*542 = 4617.8 dollars

Average profit of Farthington = 653*7.25 = 4734.5 dollars

Thurs Roger Hunt should buy Farthington

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