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		25			0.20
Moderate response		40			0.30
High response		55			0.20
Very high response		60			0.30

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

Question a:

Expected Value of Unit Sales = Σ ( Unit Sales * Probability)

= (25 * 0.20) + (40 * 0.30) + (55 * 0.20) + (60 * 0.30)

= 5 + 12 + 11 + 18

= 46

Therefore, Expected Value of unit sales is 46

Question b:

Variance of unit sales = Σ [(Units sales - Expected Value)^2 * Probability]

= [(25 - 46)^2* 0.20] + [(40 - 46)^2 * 0.30] + [(55 - 46)^2* 0.20] + [(60 - 46)^2 * 0.30]

= 88.2 + 10.8 + 16.2 + 58.8

= 174

Standard deviation of unit sales = Squareroot of Variance of unit sales

= (174)^(1/2)

= 13.190906

Theresore, standard deviation of unit sales is 13.19