Carson 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

Quizplus · Accepted Answer

Using the formula for the standard deviation of a population: 
σ = √(Σ(xi-μ)²/N), 
where xi is the return, μ is the expected value of the returns, and N is the number of returns.

First, calculate the expected value:
Expected value = (0.25 x 30%) + (0.5 x 15%) + (0.25 x 5%) = 13.75%

Next, calculate the variance:
Variance = (0.25 x (30%-13.75%)²) + (0.5 x (15%-13.75%)²) + (0.25 x (5%-13.75%)²)
= 28.7%

Finally, calculate the standard deviation:
Standard deviation = √(28.7%) = 18.62%

Therefore, the standard deviation of the estimated returns is 18.62%, which is option B.