The probability that a randomly selected data from a normally
distributed dataset with mean of μ, and standard deviation of σ, is less than a value x is given by:
[tex]P(X\leq x)=P\left(z\ \textless \ \frac{x-\mu}{\sigma} \right)[/tex]
Given that a
security with normally distributed returns has an annual expected
return of 18% and a standard deviation of 23%.
[tex]\mu=18\% \\ \\ \sigma=23\%[/tex]
The probability of getting a
return of -28% or lower in any one year is given by:
[tex]P(X\leq x)=P\left(z\ \textless \ \frac{x-\mu}{\sigma} \right) \\ \\ P\left(z\ \textless \ \frac{-28-18}{23} \right)=P(z\ \textless \ -2) \\ \\ =\bold{0.0228}[/tex]
