Question

5.3 Recently, a regional automobile dealership sent out fliers to perspective customers indicating that they had already won one of three different prizes: an automobile valued at $25,000, a $100 gas card, or a $5 Walmart shopping card. To claim his or her prize, a prospective customer needed to present the flier at the dealership's showroom. The fine print on the back of the flier listed the prob- abilities of winning. The chance of winning the car was 1 out of 31,478, the chance of winning the gas card was 1 out of 31,478, and the chance of winning the shopping card was 31,476 out of 31,478 a. How many fliers do you think the automobile dealership sent out? b. Using your answer to (a) and the probabilities listed on the flier, what is the expected value of the prize won by a prospec- tive customer receiving a flier? c. Using your answer to (a) and the probabilities listed on the flier, what is the standard deviation of the value of the prize won by a prospective customer receiving a flier? d. Do you think this is an effective promotion? Why or why not?

Answer 1

a.

The automobile dealership sent out 31,478 fliers because the total number of prizes are 31,478 and every prospective customer who received a flier must get a prize. So, the number of fliers cannot be more than the number of prizes.

b.

Expected value of the prize, E(X) =$\Sigma (Pi. Xi)$ =1/31,478($25,000)+1/31,478($100)+31,476/31,478($5) =$5.80

c.

Standard deviation value of the prize, $\sigma (X) =\sqrt{\Sigma [Pi (Xi-E(X)) ^2]}$ =$140.90

d.

Yes. This is an effective promotion as the customers are prospective and are more likely to visit the dealership's showroom to claim their prize as the prize is compulsory for every customer who received the flier.

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Answer 2

a.      How   many fliers do you think the automobile dealership sent out?