A regional automobile dealership sent out fliers to prospective customers indica

Question

A regional automobile dealership sent out fliers to prospective customers indicating that they had already won one of three different prizes: an automobile valued at $28,000, a $75 gas card, or a $55 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 probabilities of winning. The chance of winning the car was 1 out of 31,052, the chance of winning the gas card was 1 out of 31,052, and the chance of winning the shopping card was 31,050 out of 31,052. Complete parts (a) through (c).

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

b) Using your answer to (a) and the probabailities listed on the flier, what is the expected value of the prize won by a prospective customer receiving a flier?

c) Using your answer to (a) and the probabailities listed on the flier, what is the standard deviation of the value of the prize won by a prospective customer receiving a flier?

Explanation / Answer

a ans) Based on the fact that the odds of winning are expressed out with a base of 31,052, you will think that the automobile dealership sent out 31,052 fliers.

b ans) the expected value of the prize =[ 28000(1)+75(1)+5(31050) ] / 31052 =$5.90

cans) standard deviation = sqrt[(28000-5.90)^2(1)+(75-5.90)^2(1)+(5-5.90)^2 (31050)] /sqrt[ 31052] =$158.86

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