Reference no: EM132855738

To examine the effectiveness of its four annual advertising promotions, a mail-order company has sent a questionnaire to each of its customers. The questionnaire asks how many of the previous year's promotions prompted orders that otherwise would not have been made. The table lists the probabilities that were derived from the questionnaire, where x is the random variable representing the number of promotions that prompted orders.

x

0

1

2

3

4

P(x)

.10

.25

.40

.20

.05

a. 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 ordering goods that otherwise would not have been purchased?

b. A previous analysis of historical records found that the mean value of orders for promotional goods is $20, with the company earning a gross profit of 20% on each order. Calculate the expected value of the profit contribution next year.

c. The fixed cost of conducting four promotions is estimated to be $15,000 with a variable cost of $3.00 per customer for mailing and handling costs. How large a customer base does the company need to cover the cost of promotion?