Magee 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.)

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

Question

Magee 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.)

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

Quizplus · Accepted Answer

The standard deviation is calculated using the formula for the standard deviation of a population: $\sigma = \sqrt{\sum (p_i \times (r_i - \mu)^2)}$, where $p_i$ is the probability, $r_i$ is the return, and $\mu$ is the expected return. Calculating this gives approximately 18.62%.

Magee Inc'S Manager Believes That Economic Conditions During the Next Year