An investment has a mean return of 15% and a standard deviation of returns equal to 10%. If returns are normally distributed, which of the following statements is least accurate? The probability of obtaining a return: A) between 5% and 25% is 0.68. B) greater than 25% is 0.32. C) greater than 35% is 0.025. Your answer: B was correct! Sixty-eight percent of all observations fall within +/- one standard deviation of the mean of a normal distribution. Given a mean of 15 and a standard deviation of 10, the probability of having an actual observation fall within one standard deviation, between 5 and 25, is 68%. The probability of an observation greater than 25 is half of the remaining 32%, or 16%. This is the same probability as an observation less than 5. Because 95% of all observations will fall within 20 of the mean, the probability of an actual observation being greater than 35 is half of the remaining 5%, or 2.5%. Is anyone able to explain this answer to me please?

Here’s a diagram of the normal distribution.

A) The mean is 15% and one standard deviation is 10%. So 15% ± 10% = (5%, 25%). Looking at the diagram, 68% of the data lies within one standard deviation

B) If the return is greater than 25% (greater than one standard deviation), it means that the return has to lie beyond one standard deviation (to the right) in the diagram above (between 1 and 3), which is 16% and not 32%.

C) Using the same logic as A and B, 35% means that the return lies within 2 standard deviations (15%+10%+10%). This means that only 2.5% of returns lies in this region, between 2 and 3.

Tell me if this makes sense, otherwise I’ll edit later to make it clearer

Perfect, thank you.

Important to remember the probability of the different standard deviations (or so everyone says)

Sir where is the diagram, I am not able to see any diagram here.

" leptokurtic distribution will have a greater % of small deviation from mean and a greater % of extremely large deviation from ". Can anybody explain me this in a simple term ?