Chapter 5, Problem 3PS

Recently , a regional automobile dealership sent out fliers to perspective customer indicating that had already won one of three different prizes: an automobile valued at $\text{\$}25,000,\text{a}\text{\$}100$ gas card, or a $\text{\$}5$ Walmart shopping card. To claim his or her prize, a prospective customer needed to present the flier at the dealership’s showroom. The print on the back of the flier listed the probabilities of winning. The chance of wining the car was 1 out 31,478, the chance of winning the gas card was 1 out of 31,478, and the shopping card was 31,476 out of 31,478.

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

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

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

d. Do you think this is an effective promotion? why or why not?