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

Question

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

Quizplus · Accepted Answer

This is a relatively technical problem. It should be used only if calculations are emphasized in class, or on a take-home exam where students have time to look up formulas or to use Excel or their calculator functions.
 
$\begin{array}{l}
\begin{array} { l } 
\text { Economic } &&\text { Return }\
\text { Conditions } & \text { Prob. } & \text { This state }\
\text { Strong } &30 \%&32.0 \%\
\text { Normal } &  40 \% & 10.0 \%  \
\text { Weak } & 30\% &-16.0\%\
&100\%&8.8\%\
\text { α= Sgrt of variance}&18.62 \%&\text { 18.62 \% by Excel }
\end{array}
\begin{array} { l } 
\text { Dev. from  } &\text { Squared  } &\text { Sqd. dev }\
\text { Mean }& \text { Dev. }& \times \text { Prob } \
23.20 \%&10.24\%& 3.07 \% \
 1.20 \% & 0.01 \% & 0.01 \% \
-24.80 \% & 6.15 \%&1.85 \%\
& \text { Variance }&4.92 \%\
\end{array}
\end{array}$

Stuart Company's Manager Believes That Economic Conditions During the Next Economic \text { Economic } Economic

Stuart Company's Manager Believes That Economic Conditions During the Next $\text { Economic }$