\"A private equity firm is evaluating two alternative investments. Although the

Question

"A private equity firm is evaluating two alternative investments. Although the returns are random, each investment’s return can be described using a normal distribution. The first investment has a mean return of $2,000,000 with a standard deviation of $125,000. The second investment has a mean return of $2,275,000 with a standard deviation of $500,000."

"c. If the firm would like to limit the probability of a return being less than $1,750,000, which investment should it make?"

Please explain why you think (a.) is the better investment. Thanks.

Explanation / Answer

Let X be a random variable denoting return of the first investment and Y be a random variable denoting return of the second investment.

X~ N(2,000,000 ,125,0002)

Y~N(2,275,000 ,500,0002)

P(X<1,750,000)=0.0227501 < P(Y<1.750,000)=0.146859

The probability of a return from 1st investment being less than $1,175,000 is less than that of probability of a return from 2nd investment.

So,second investment is better.

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