Question

4. Exercise 2.5

The demand for MICHTEC's products is related to the state of the economy. If the economy is expanding next year (an above-normal growth in GNP), the company expects sales to be $90 million. If there is a recession next year (a decline in GNP), sales are expected to be $75 million. If next year is normal (a moderate growth in GNP), sales are expected to be $85 million. MICHTEC's economists have estimated the chances that the economy will be either expanding, normal, or in a recession next year at 0.1, 0.6, and 0.3, respectively.

The expected annual sales is $82.5   million.

The standard deviation of annual sales is: _______ million? Choices for this fill in the blank is as followed:  A. 3.06 million, B. 5.12 million, or C. 4.54 million?

The coefficient of variation of annual sales is______? Choices for this fill in the blank are as followed: A. 0.037 B. 0.309 C. 0.062

Answer 1

Solution:

1. To find the standard deviation, we first find the variance of annual sales:

Variance = E(X²) - (E(X))², X is simply value of sales

We are already given expected value, E(X) = $82.5m

E(X²) = sum(probability*value²)

E(X²) = 0.1*(90)² + 0.6*(85)² + 0.3*(75)² = $6832.5m

So, V(X) = 6832.5 - 82.5² = $26.25m

And, standard deviation becomes: (V(X))^1/2 = 26.25^0.5 = $5.123m

Thus, correct option is (B).

2. Coefficient of variation, CV = (standard deviation/expected (or mean) value)*100

CV = (5.12/82.5)*100 = 6.21% or 0.062

Thus, correct option is (C).

answered by: anonymous