Calculate the standard deviation of the expected dollar returns for Ditto Copier Center, given the following distribution of returns: Probability Return
0)2 $50
0)5 $20
0)3 −$15
A)$36.0
B)$23.0
C)$18.0
D)$13.0
E)$30.0

Question

Quizplus · Accepted Answer

To calculate the standard deviation, we need to use the formula:

Standard Deviation = sqrt[∑(Ri - Rmean)2 * Pi]

Where:
Ri = return for each probability
Rmean = expected return (weighted average)
Pi = probability for each return

First, let's calculate the expected return:
Expected Return = (0.2 x $50) + (0.5 x $20) + (0.3 x -$15) = $15

Now, we can use the formula to calculate the standard deviation:

Standard Deviation = sqrt[( ($50 - $15)^2 x 0.2) + ( ($20 - $15)^2 x 0.5) + ( (-$15 - $15)^2 x 0.3)]

Standard Deviation = sqrt[(1225 x 0.2) + (25 x 0.5) + (900 x 0.3)]

Standard Deviation = sqrt[245 + 12.5 + 270]

Standard Deviation = sqrt[527.5]

Standard Deviation ≈ $23.0

Therefore, the best choice is B, with a standard deviation of approximately $23.0.

Calculate the Standard Deviation of the Expected Dollar Returns for Ditto