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:

Possiable Market Reaction Sales in Units Probabilites

Low Response 20 0.10

Moderate Response 40 0.30

Hight Response 55 0.40

Very High Response 70 0.20

a. What is the expected value of sales for the new product?

b. What is the standard deviation of unit sales?

a. Expected value of unit sales for the new product = 20*0.10 + 40*0.30 + 55*0.40 + 70*0.20 = 2+12+22+14 = 50 units

b.

Low response sales in units = 20:

Deviation from the expected value of 50 sales: - 30

(Sales-50) ^2 = 900

Probability = 0.10

Probability * (Sales-50) ^2 = 0.10*900 = 90

Moderate response sales in units = 40:

Deviation from the expected value of 50 sales: - 10

(Sales-50) ^2 = 100

Probability = 0.30

Probability * (Sales-50) ^2 = 0.30*100 = 30

High response sales in units = 55:

Deviation from the expected value of 50 sales: 5

(Sales-50) ^2 = 25

Probability = 0.40

Probability * (Sales-50) ^2 = 0.40*25 = 10

Very High response sales in units = 70:

Deviation from the expected value of 50 sales: 20

(Sales-50) ^2 = 400

Probability = 0.20

Probability * (Sales-50) ^2 = 0.20*400 = 80

Variance = 90+30+10+80 = 210

Standard deviation = root of 210 = 14.49