Question

Problem 13-3 Expected value and standard deviation [LO13-1] Sampson Corp. is evaluating the introduction of a new product. The possible levels of unit sales and the probabilities of their occurrence are shown next: Possible Market Reaction Sales in Units Probabilities Low response 50 .50 Moderate response 80 .30 High response 100 .10 Very high response 110 .10 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

1. The expected unit sales are:

U=∑ni=1pi∗UiU¯=∑i=1npi∗Ui, where p_i is the probability of units U_i

U = .5*50+.3*80+.10*100+.10*110

= 25 + 24 + 10 + 11

= 70

Expected unit sales is 70

2. The formula for SD is:

σ=√∑ni=1pi∗(Ui−¯U)^2

= square root of 0.5*(50-70)^2 + 0.3*(80-70)^2 + .10*(100-70)^2 + .10*(110-70)^2

= square root of 200 + 30 + 90 + 160

Square root of 480

= 21.91 units

The SD is 21.91 units