Stuart Company'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.) $\begin{array}{llr}\text { Economic }\
\text { Conditions }&\text { prob. }&\text {Return }\\hline
\text { Strong } & 30 \% & 32.0 \% \
\text { Normal } & 40 \% & 10.0 \% \
\text { Weak } & 30 \% & -16.0 \%
\end{array}$
A) 17.69%
B) 18.62%
C) 19.55%
D) 20.52%
E) 21.55%

Question

Quizplus · Accepted Answer

To calculate the standard deviation of the estimated returns, first, we find the expected return (mean), then use it to calculate the variance, and finally take the square root of the variance to get the standard deviation.1. Calculate the expected return (mean):$$E(R) = (0.30 \times 32\%) + (0.40 \times 10\%) + (0.30 \times (-16\%)) = 9.6\% + 4\% - 4.8\% = 8.8\%$$2. Calculate the variance:$$Var(R) = (0.30 \times (32\% - 8.8\%)^2) + (0.40 \times (10\% - 8.8\%)^2) + (0.30 \times (-16\% - 8.8\%)^2)$$$$Var(R) = (0.30 \times (23.2\%)^2) + (0.40 \times (1.2\%)^2) + (0.30 \times (-24.8\%)^2)$$$$Var(R) = (0.30 \times 0.053824) + (0.40 \times 0.000144) + (0.30 \times 0.061504)$$$$Var(R) = 0.0161472 + 0.0000576 + 0.0184512 = 0.034656$$3. Calculate the standard deviation:$$SD(R) = \sqrt{Var(R)} = \sqrt{0.034656} = 0.1862 = 18.62\%$$Therefore, the correct answer is B) 18.62%.

Stuart Company's Manager Believes That Economic Conditions During the Next