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		10			.20
Moderate response		50			.30
High response		70			.40
Very high response		90			.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.)

	Expected value units

b. What is the standard deviation of unit sales? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

	Standard deviation units

Answer 1

(a) Expected value = sales in units * probabilities

Expected value = (10 * 0.20) + (50 * 0.30) + (70 * 0.40) + (90 * 0.1)

Expected value = 2 + 15 + 28 + 9 = 54

(b) Standard deviation:

For calculating standard deviation, first we will calculate (X - EX)², where, X is the sales in units and EX is the expected value as calculated in point (a)

Low response: (10 - 54)² = (-44)² = 1936

Moderate response: (50 - 54)² = (-4)² = 16

High response: (70 - 54)² = (16)² = 256

Very high response: (90 - 54)² = (36)² = 1296

In the next step, we will multiply the respective probabilities to the solution above, as per below,

Low response: 1936 * 0.2 = 387.2

Moderate response: 16 * 0.3 = 4.8

High response: 256 * 0.4 = 102.4

Very high response: 1296 * 0.1 = 129.6

In the next step, we will add up the above numbers computed as below:

387.2 + 4.8 + 102.4 + 129.6 = 624

Now, standard deviation is the square root of the above number computed:

Standard deviation = (624)^1/2 = 24.98