Question

knowing a rate of return of 6% and a standard deviation of 13%. What percentage of returns were greater than 45%

Answer 1

Assume that returns of this portfolio $X$ follow a Normal distribution: $X\sim N(\mu, \sigma^2).$

Then $Z=\dfrac{X-\mu}{\sigma}\sim N(0, 1)$

Given that $\mu=0.06, \sigma=0.13.$

$$P(X>0.45)=1-P(X\leq0.45)=1-P(Z\leq{0.45-0.06\over 0.13})=$$ $$=1-P(Z\leq3)\approx1-0.998650\approx0.001350$$

$0.135\%$