Over a number of years, the average annual rate of return for Fidelity's Capital Appreciation mutual fund has been .17 with a standard deviation of .35.Assume annual returns are approximately normally distributed around the average rate.Using this historical information as the basis for the calculation, there is a 20% probability that this fund will have a return greater than or equal to how much?
A)-.124
B).198
C).464
D).3732
E)-.293

Question

Quizplus · Accepted Answer

To find the return corresponding to a 20% probability of being exceeded, we look for the z-score associated with the top 20% of a normal distribution. This z-score is approximately 0.84. Using the z-score formula $Z = \frac{(X - \mu)}{\sigma}$, where $X$ is the return we're solving for, $\mu = 0.17$ is the mean, and $\sigma = 0.35$ is the standard deviation, we rearrange to solve for $X$: $X = Z\sigma + \mu$. Substituting the values, $X = 0.84(0.35) + 0.17 = 0.294 + 0.17 = 0.464$.

Over a Number of Years, the Average Annual Rate of Return