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.
a. How likely is it that the first investment will return $1,900,000 or less?
b. How likely is it that the second investment will return $1,900,000 or less?
c. If the firm would like to limit the probability of a return being less than $1,750,000, which investment should it make?