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).

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

answer; specific performance;