A group of investors wants to be sure to always earn at least a 5% rate of return on their investments. They are looking at an investment that has a normally distributed probability distribution with an expected rate of return of 10% and a standard deviation of 5%. The probability of meeting or exceeding the investors’ desired return in any given year is closest to:

A) 84%. CORRECT ANSWER

B) 98%.

C) 34%.

Explanation References The mean is 10% and the standard deviation is 5%. You want to know the probability of a return 5% or better. 10% - 5% = 5% , so 5% is one standard deviation less than the mean. Thirty-four percent of the observations are between the mean and one standard deviation on the downside. Fifty percent of the observations are greater than the mean. So the probability of a return 5% or higher is 34% + 50% = 84%.

**Could someone please explain how / why it’s 50% on the upside and not 34% as the downside. Where did the extra 16% come from?!**