Asked by Claudia Reyes on May 27, 2024
Verified
Refer to Table 5.4. If at Job B the $20 outcome occurs with probability .2, and the $50 outcome occurs with probability .8, then the standard deviation of payoffs at Job B is nearest which value?
A) $10
B) $12
C) $20
D) $35
E) $44
Standard Deviation
A statistical measure that quantifies the amount of variation or dispersion of a set of data values from the mean.
- Comprehend the approach for determining standard deviation as an indicator of risk.
Verified Answer
HB
Haapppyy BAAABBBSSSYYYMay 28, 2024
Final Answer :
B
Explanation :
To calculate the standard deviation of payoffs at Job B, we first need to calculate the expected payoff:
Expected payoff = (probability of $20 outcome x $20) + (probability of $50 outcome x $50)
Expected payoff = (.2 x 20) + (.8 x 50)
Expected payoff = $44
To calculate the standard deviation, we need to find the variance first:
Variance = [(probability of $20 outcome x ($20 - expected payoff)^2) + (probability of $50 outcome x ($50 - expected payoff)^2)]
Variance = [(.2 x (20-44)^2) + (.8 x (50-44)^2)]
Variance = [(.2 x 576) + (.8 x 36)]
Variance = 146.4
Standard deviation = square root of variance = sqrt(146.4) = 12
Therefore, the standard deviation of payoffs at Job B is nearest to $12. Answer choice B is correct.
Expected payoff = (probability of $20 outcome x $20) + (probability of $50 outcome x $50)
Expected payoff = (.2 x 20) + (.8 x 50)
Expected payoff = $44
To calculate the standard deviation, we need to find the variance first:
Variance = [(probability of $20 outcome x ($20 - expected payoff)^2) + (probability of $50 outcome x ($50 - expected payoff)^2)]
Variance = [(.2 x (20-44)^2) + (.8 x (50-44)^2)]
Variance = [(.2 x 576) + (.8 x 36)]
Variance = 146.4
Standard deviation = square root of variance = sqrt(146.4) = 12
Therefore, the standard deviation of payoffs at Job B is nearest to $12. Answer choice B is correct.
Learning Objectives
- Comprehend the approach for determining standard deviation as an indicator of risk.