# Standard Deviation from the Mean

Working through a Schweser mock, and I can’t figure out how this answer is correct…

An investment has a mean return of 15% and a standard deviation of returns equal to 10%. If the distribution of returns is approximately normal, which of the following statements is least accurate? The probability of obtaining a return:

A) less than 5% is about 16%.

B) greater than 35% is about 2.5%.

C) between 5% and 25% is about 95%.

Answer C - About 68% of all observations fall within ±1 standard deviation of the mean. Thus, about 68% of the values fall between 5 and 25.

I don’t get it. I went with A, as if the standard deviation is 10%, one down from 15% is 5%, and one up from there is 25%. If 68% will fall within 1sd, then that means 32% will be either below 5% or above 25%, therefore less than 5% is 16%.

I’ve not been firing on all cyclinders today so I’m assuming I’m just missing something obvious, but I don’t get how they come up with the answer C.

argghh!! Literally as soon as I clicked ‘add comment’ I noticed it said ‘least accurate’. I’ll leave this up as a reminder to everyone to read the question properly. I just spent 10mins staring at this trying to figure it out.