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.)

a. The expected value of unit sales for the new product can be calculated by multiplying each level of unit sales with its respective probability and then summing up these products.

Expected value (E) = Σ (probability of each outcome * respective unit sales)

E = (0.30 * 20) + (0.20 * 35) + (0.20 * 50) + (0.30 * 90)

E = (6) + (7) + (10) + (27)

E = 50 units

So, the expected value of unit sales for the new product is 50 units.

b. The standard deviation of unit sales indicates the variability or spread of unit sales figures from their expected value.

First, we need to find the variance, which is the square of the standard deviation. Variance (σ^2) is calculated by summing the squared differences between each outcome and the expected value, each weighted by its probability.

Variance (σ^2) = Σ (probability of each outcome * (respective unit sales - expected value)^2)

Variance (σ^2) = (0.30 * (20 - 50)2) + (0.20 * (35 - 50)2) + (0.20 * (50 - 50)2) + (0.30 * (90 - 50)2)

Variance (σ^2) = (0.30 * 900) + (0.20 * 225) + (0.20 * 0) + (0.30 * 1600)

Variance (σ^2) = 270 + 45 + 0 + 480

Variance (σ^2) = 795

Now, to find the standard deviation (σ), we take the square root of the variance:

σ = √795

Calculating that we get,

σ = 28.21

So the standard deviation of unit sales is approximately 28.21 units.