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

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

Quizplus · Accepted Answer

Using the formula for the standard deviation of a population, we have:
\begin{align*}
\sigma &= \sqrt{\sum p_i (x_i -\mu)^2}\
&= \sqrt{(0.3)(0.32-0.06)^2+(0.4)(0.1-0.06)^2+(0.3)(-0.16-0.06)^2}\
&= \sqrt{(0.3)(0.26)^2+(0.4)(0.04)^2+(0.3)(-0.22)^2}\
&= \sqrt{0.020148}\
&= 0.4486\
&= 18.62\%
\end{align*}
Therefore, the standard deviation of the estimated returns is 18.62%. So, the best choice is B.

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