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

Question

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

Quizplus · Accepted Answer

To find the standard deviation, first calculate the expected return: $ E(R) = (0.3 \times 32) + (0.4 \times 10) + (0.3 \times -16) = 8.8\% $. Then, calculate the variance: $ \sigma^2 = (0.3 \times (32 - 8.8)^2) + (0.4 \times (10 - 8.8)^2) + (0.3 \times (-16 - 8.8)^2) = 346.44 $. Finally, the standard deviation is the square root of the variance: $ \sigma = \sqrt{346.44} = 18.62\% $.

Carson Inc A) 1769% B) 18

Carson Inc A) 1769%
B) 18