, To examine the effectiveness of its five annual advertising promotions, a mail-order company has sent a questionnaire to each of its customers, asking how many of the previous year's promotions prompted orders that otherwise would not have been made. The following table summarizes the data received, where the random variable X is the number of promotions indicated in the customers' responses: 1 2 3 4 1- (y/100+0.25+0.2+0.05+z/100) | 0.2 P(X=x) y/100 In the above table: y, z are the last two digits of your student code (for example: if a student code is 17071365 then y = 6, z = 5). A previous analysis of historical data found that the mean value of orders for promotional goods is $20, with the company earning a gross profit of 20% on each order. It is assumed that customer behavior next year will be the same as last year, and the fixed cost of conducting the five promotions next year is estimated to be $15000, with a variable cost of $3 per customer for mailing and handling costs. a/ Find expected value of X, variance of X and the expected gross profit per customer next year. b/ How large a customer base must the company have to cover the cost of the promotions? 0.25 0.05 z/100