Question

Myers Business Systems is evaluating the introduction of a new product. The possible levels of unit sales and the probabilities of their occurrence are given next: Possible Market Reaction Sales in Units Probabilities Low response 20 .30 Moderate response 35 .20 High response 50 .20 Very high response 90 .30
a. What is the expected value of unit sales for the new product? (Do not round intermediate calculations and round your answer to the nearest whole unit.)
b. What is the standard deviation of unit sales? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Answer:

a. What is the expected value of unit sales for the new product? (Do not round intermediate calculations and round your answer to the nearest whole unit.)

Possible Market Reaction    Sales Units     Probability     Expected sales

Low response                             20                 .30                    6

Moderate response                    35                 .20                    7

High response                            50                 .20                    10

Very high response                    90                 .30                    27          

Total                                                                                          50 units

b. What is the standard deviation of unit sales? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

mean = (6 + 7 + 10 + 27) / 4  = 12.5

variance = {[0.30 x (20 - 50)²] + [0.20 x (35 - 50)²] + [0.20 x (50 - 50)²] + [0.30 x (90 - 50)²]} / 4 = (270 + 45 + 0 + 480) / 4 = 795 / 4 = 198.75

standard deviation = √198.75 = 14.10 units