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 ​$25,000​ a ​$100 gas​ card, or a ​$5 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 31,070​, the chance of winning the gas card was 1 out of 31,070 and the chance of winning the shopping card was 31,068 out of 31,070. Complete parts​ (a) through​ (d).

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

Using your answer to​ (a) and the probabilities listed on the​ flier, what is the expected value of the prize won by a prospective customer receiving a​ flier? (Round to nearest cent)

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? (Round to nearest cent)

Do you think this is an effective​ promotion? Why or why​ not?

A. No. The promotion will not turn a profit regardless of how many customers redeeming fliers make a purchase.

B. Yes. The promotion will turn a profit if any of the customers redeeming fliers make a​ purchase, which is likely.

C. Yes. The promotion will turn a profit if the customers redeeming fliers make an average purchase greater than the expected value of the prize​ won, which is likely.

D. No. The promotion will only turn a profit if the customers redeeming fliers make an average purchase less than the expected value of the prize​ won, which is unlikely.

Answer 1

a)

number of fliers =31070

b)

x	P(X=x)	xP(x)	x2P(x)
25000	1/31070	0.80463	20115.86740
100	1/31070	0.00322	0.32185
5	31068/31070	4.99968	24.99839
total		5.8075	20141.1876
	E(x) =μ=	ΣxP(x) =	5.8075
	E(x2) =	Σx2P(x) =	20141.1876
	Var(x)=σ2 =	E(x2)-(E(x))2=	20107.460220
	std deviation=	σ= √σ2 =	141.80078

expected value =5.81

standard deviation of the value =141.80

B. Yes. The promotion will turn a profit if any of the customers redeeming fliers make a​ purchase, which is likely.