Recently, a regional automobile dealership sent out fliers to perspective customers, indicating that they had already won one of three different prizes: a 2008 Kia Optima valued at $15,000, a $500 gas card, or a $5 Wal-Mart 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 31,478, the chance of winning the gas card was 1 out of 31,478 and the chance of winning the shopping card was 31,476 out of 31,478. 

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?