What is the standard deviation of the payoff from an investment that yields $5,000 with a probability of 0.15 and $500 with a probability of 0.85?
A) $0
B) $2,581,875
C) $42.50
D) $1,606.82

Question

Quizplus · Accepted Answer

The formula for calculating the standard deviation of a discrete probability distribution is:

σ = sqrt [ ∑(xi - μ)2 * P(xi) ]

where:
xi = the value of each possible outcome
μ = the expected value (mean) of the distribution
P(xi) = the probability of each outcome

Using this formula, we can calculate the standard deviation for this investment:

σ = sqrt [ ((5000-1125)2 * 0.15) + ((500-1125)2 * 0.85) ]
     = sqrt [ (3437500 * 0.15) + (437500 * 0.85) ]
     = sqrt [ 515625 + 371875 ]
     = sqrt [ 887500 ]
     = $1,606.82

Therefore, the answer is D, $1,606.82.

What Is the Standard Deviation of the Payoff from an Investment