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.) $\begin{array}{c}
\begin{array}{lll}
\text {Economic}\
\underline{\text {Conditions}}\
\text {Strong}\
\text {Normal}\
\text {Weak}
\end{array}
\begin{array}{lll}
\
\underline{\text {Prob.}}\
30 \% \
40 \% \
30 \%
\end{array}
\begin{array}{lll}
\
\underline{\text {Return}}\
\ 32.0 \% \
10.0 \% \
-16.0 \%
\end{array}
\end{array}$

A)17.69%
B)18.62%
C)19.55%
D)20.52%
E)21.55%

Question

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.) $\begin{array}{c}
\begin{array}{lll}
\text {Economic}\
\underline{\text {Conditions}}\
\text {Strong}\
\text {Normal}\
\text {Weak}
\end{array}
\begin{array}{lll}
\
\underline{\text {Prob.}}\
30 \% \
40 \% \
30 \%
\end{array}
\begin{array}{lll}
\
\underline{\text {Return}}\
\ 32.0 \% \
10.0 \% \
-16.0 \% 
\end{array}
\end{array}$

A)17.69%
B)18.62%
C)19.55%
D)20.52%
E)21.55%

Quizplus · Accepted Answer

To calculate the standard deviation of the estimated returns, we first need to find the expected return (mean) and then use the formula for the standard deviation of a population. 1. Calculate the expected return (mean):$$ \text{Expected Return} = (0.30 \times 32\%) + (0.40 \times 10\%) + (0.30 \times -16\%) = 9.6\% + 4\% - 4.8\% = 8.8\% $$2. Calculate each condition's squared deviation from the mean, multiply by its probability, and sum these values:$$ \text{Variance} = (0.30 \times (32\% - 8.8\%)^2) + (0.40 \times (10\% - 8.8\%)^2) + (0.30 \times (-16\% - 8.8\%)^2) $$$$ = (0.30 \times (23.2\%)^2) + (0.40 \times (1.2\%)^2) + (0.30 \times (-24.8\%)^2) $$$$ = (0.30 \times 0.053824) + (0.40 \times 0.000144) + (0.30 \times 0.061504) $$$$ = 0.0161472 + 0.0000576 + 0.0184512 = 0.034656 $$3. Calculate the standard deviation (the square root of the variance):$$ \text{Standard Deviation} = \sqrt{0.034656} = 0.1862 \text{ or } 18.62\% $$Therefore, the standard deviation of the estimated returns is 18.62%.

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