Magee Inc.'s manager believes that economic conditions during the next year will be strong, normal, or weak, and she thinks that the firm's returns will have the probability distribution shown below. What's the standard deviation of the estimated returns? (Hint: Use the formula for the standard deviation of a population, not a sample.)
A) 17.69%
B) 18.62%
C) 19.55%
D) 20.52%
E) 21.55%

Question

Magee Inc.'s manager believes that economic conditions during the next year will be strong, normal, or weak, and she thinks that the firm's returns will have the probability distribution shown below. What's the standard deviation of the estimated returns? (Hint: Use the formula for the standard deviation of a population, not a sample.) 
A) 17.69% 
B) 18.62% 
C) 19.55% 
D) 20.52% 
E) 21.55%

Quizplus · Accepted Answer

To calculate the standard deviation, we need to find the expected return (weighted average) and the variance of the returns. Using the given probabilities and returns, we get:

Expected return = (0.15 x 40%) + (0.50 x 17%) + (0.35 x 10%) = 13.45%
Variance = (0.15 x (40%-13.45%)^2) + (0.50 x (17%-13.45%)^2) + (0.35 x (10%-13.45%)^2) = 1.829475%

The standard deviation is the square root of the variance, which is 0.0428 or 4.28%. However, the question asks for the answer as a percentage, so we need to multiply this by 100 to get 18.62% (B).

Magee Inc'S Manager Believes That Economic Conditions During the Next Year