# Quants Help

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:

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?!

The probability that a normally random variable is greater than μ − σ is 84%.

The answer states that the probability of a return 5% or higher is 34% + 50% = 84%

How was the 50% calculated? Why is it not 34% since 15% is also one standard deviation above the mean of 10%?

50% is the probability that the return is above the mean.

34% is the probability that the return is between μ − σ and μ.

How was the 50% probability above the mean calculated?

According to normal distribution diagram, 50% are on the left and 50% on the right from mean. Since 5% lies on the left we’ll take only the area before 5%, and whole area on the right since all of them are higher than mean.

Got it, thank you!

Normal distributions are symmetric about the mean.