Question

The historical returns on a portfolio had an average return of 15 percent and a standard deviation of 18 percent. Assume that returns on this portfolio follow a bell-shaped distribution. a. Approximately what percentage of returns were greater than 33 percent? (Round your answer to the nearest whole percent.) Percentage of returns b. Approximately what percentage of returns were below –21 percent? (Round your answer to 1 decimal place.) Percentage of returns

Answer 1

$mu-3sigma=15-(3*18)=-39$

$mu-1sigma=15-(1*18)=-3$

$mu=15$

$\mu+3\sigma=15+(3*18)=69$

$below\; -21 \;percent \Rightarrow P(X<-21)=2.35&plus;0.15=\mathbf{{\color{Red} 2.5}}$