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		20			.30
Moderate response		35			.20
High response		45			.20
Very high response		60			.30

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

Answer 1

Solution

1. Determination of standard deviation of unit sales:

Standard deviation

Steps –

1. Determine the mean
2. For each value subtract the mean and square the result
3. Determine the mean of the squared values
4. Determine the square root of the squared values

Step 1 –

	determination of mean
	sales in units D	probabilities P	expected sales DP
Low response	20	0.3	6
Moderate response	35	0.2	7
High response	45	0.2	9
Very high response	60	0.3	18
Mean (expected sales)			41

	sales in units D	expected sales DP	Difference, D - Mean)	Squares of difference	probabilities P	Probabilities
Low response	20	6	-21	441	0.3	132.3
Moderate response	35	7	-6	36	0.2	7.2
High response	45	9	4	16	0.2	3.2
Very high response	60	18	19	361	0.3	103.3
Mean (expected sales)		41				251
	standard deviation, = square root of 251 = 15.84 units