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 $544, and the average profit per car at Farthington Auto Sales is $654. (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   ____.

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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 $544, and the average profit per car at Farthington Auto Sales is $654.

(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   ____.

 

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