Table 5.4

-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

Question

Table 5.4
 
-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

Quizplus · Accepted Answer

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.

Table 5.4 -Refer to Table 5.4. If at Job B the $20