A local airline sent out an advertisement via email to its potential customers. It stated that the airline would be holding a lucky draw in which the prizes would be (i) fifteen airline tickets or $1,500 in cash, (ii) five airline tickets or $500 in cash, and (iii) three dollar as coupons redeemable at local gas stations. The fine print on the advertisement voucher indicated the probabilities of winning. The chance of winning (i) was 1 out of 42,376, (ii) was 1 out of 42,376, and (iii) was 42,374 out of 42,376.

a. How many emails do you think the airline sent out?

b. Using the answer for part (a) and the probabilities listed in the fine print of the email, what is the expected value of the prize won by a prospective customer?

c. Using the answer of for part (a) and the probabilities listed in the email, what is the standard deviation of the value of the prize won by a prospective customer?

d. Do you think this is an effective promotion? Explain.