Question

Given a normal distribution, assume you want to earn a rate of return that plots more than three standard deviations above the mean. What is your probability of earning such a return in any one year?

A. Between 0.5% and 1%
B. Between 1% and 5%
C. 0%
D. Not enough information
E. Less than 0.5%

Answer 1

Explanation:

In a normal distribution, approximately 99.7% of the data falls within three standard deviations of the mean if the distribution is symmetric. Therefore, the probability of earning a rate of return more than three standard deviations above the mean is very low.

Options A and B suggest that the probability is between 0.5% and 5%. However, since we are more than three standard deviations above the mean, the probability is closer to the tail end, which is much smaller than 5%.

The correct answer is:

E. Less than 0.5%