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 comma 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 comma 248​, the chance of winning the gas card was 1 out of 31 comma 248 comma and the chance of winning the shopping card was 31 comma 246 out of 31 comma 248. Complete parts​ (a) through​ (c).

Answer 1

Answer:

the requirements are missing, so I looked for a similar question.

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 prospective 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?

a) the total fliers sent out = 31,246 + 1 + 1 = 31,248

b) expected value = [(1 x $28,000) + (1 x $100) + (31,246 x $5)] / 31,248 = $5.90

c) σ² = [($28,000 - $5.90)² x 1] + [($100 - $5.90)² x 1] + [($5 - $5.90)² x 31,246] / 31,248 = ($783,669,634.80 + $8,854.81 + $25,309.26) / 31,248 = $25,080.13

σ = √$25,080.13 = $158.37