A private equity firm is evaluating two alternative investme

\"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.

Solution

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.