# Probabilities and Market Response

1) Brax Technology Corporation is evaluating the introduction of a new product. The possible levels of unit sales and the probabilities of their occurrence are given.

Possible

market reaction Sales in units Probabilities

Low response 30 .10

Moderate response 40 .10

High response 55 .20

Very high response 65 .60

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(a) What is the expected value of unit sales for the new product? (Round your answer to 2 decimal places.)

(b) What is the standard deviation of unit sales? (Round your final answer to 2 decimal places.)

2) Salome Builders Limited is evaluating a new promotional campaign that could increase home sales. Possible outcomes and probabilities of the outcomes are shown below.

Possible outcomes Additional sales in units Probabilities

Ineffective campaign 20 .40

Normal response 110 .40

Extremely effective 140 .20

________________________________________

(a) Compute the coefficient of variation. (Round your answer to 3 decimal places.)

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#### Solution Preview

1)

(a) Expected Value = 57

X P X*P

30 0.1 3.00

40 0.1 4.00

55 0.2 11.00

65 0.6 39.00

Expected Value=?[X*P] = 57.00

(b) Standard Deviation = 11.87

Recall:

Standard Deviation=?((X-E(X))^2*P)

X E(X) (X-E(X)) (X-E(X))2 P P*[(X-E(X))]^(2)

30 57.00 ...

#### Solution Summary

The following posting discusses probabilities and market responses. Step by step calculations are given for each.