Question

Shack Homebuilders Limited is evaluating a new promotional campaign that could increase home sales. Possible outcomes and probabilities of the outcomes are shown next.

Possible Outcomes Additional

Sales in Units Probabilities

Ineffective campaign 60 .20

Normal response 80 .40

Extremely effective 140 .40

Compute the coefficient of variation. (Do not round intermediate calculations. Round your answer to 3 decimal places.)

Answer 1

Coefficienct of Variation = Std deviation/Expected Return

Let us first calculate the expected return.

E[R] = (0.20 * 60) + (0.40 * 80) + (0.40 * 140) = 12 + 32 + 56 = 100

Now, we need to calculate the standard deviation.

Probability	Value	Squared Deviation from Expected Value
0.2	60	= (60 - 100)^2 = 1600
0.4	80	= (80 - 100)^2 = 400
0.4	140	= (140 - 100)^2 = 1600

Variance = (0.2 * 1600) + (0.4 * 400) + (0.4 * 1600) = 1,120

Standard deviation = square root of variance

= 33.47

Coefficient of Variation = 33.47/100 = 0.3347 (this is in absolute form, 33.47% in % form)