$3\mathrm{.}8$ CAPM. The Capital Asset Pricing Model $($CAPM$)$ is a financial model that assumes returns

on a portfolio are normally distributed. Suppose a portfolio has an average annual return of $14\mathrm{.}7\%$

$($i$.$e$.$ an average gain of $14\mathrm{.}7\%)$ with a standard deviation of $33\%.$ A return of $0\%$ means the

value of the portfolio doesn$$t change, a negative return means that the portfolio loses money, and

a positive return means that the portfolio gains money.

$($a$)$ What percent of years does this portfolio lose money, i$.$e$.$ have a return less than $0\%?$

$($b$)$ What is the cutoff for the highest $15\%$ of annual returns with this portfolio?