(Solved): To examine the effectiveness of its four annual advertising promotions, a mail order company has se ...

To examine the effectiveness of its four 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 would not have otherwise been made. The accompanying table lists the probabilities that were derived from the questionnaire, where $X$ is the random variable representing the number of promotions that prompted orders. If we assume that overall customer behavior next year will be the same as last year, what is the expected number of promotions that each customer will take advantage of next year by ordering goods that otherwise would not be purchased? Expected value $=$ A previous analysis of historical records found that the mean value of orders for promotional goods is 20 dollars, with the company earning a gross profit of $20\%$ on each order. Calculate the expected value of the profit contribution next year. Expected value $=$ The foxed cost of conducting the four promotions is estimated to be 14000 dollars with a variable cost of 5.5 dollars per customer for mailing and handling costs.