A retail client of yours is interested in knowing how high an annual return a major stock index might have, as a once-in--twenty-years event. The index in question has had an annual return of 11% with a standard deviation of 22%. You believe these returns have been normally distributed. What is the highest return that could be expected once in twenty years?

Explanation: Once in twenty years is 1/20 = 5%. So the client seeks the 95th percentile return. This could be obtained by computing a 95% confidence interval. However, since our information will be based at the mean, we should seek the 90% confidence interval, where the other 10% is split between the lower and upper bounds of the distribution. That way, we can obtain the upper 5% figure. The upper bound of the 90% confidence interval is 11% + 22%*1.645 = 47.2%.