Assume that the equity risk premium is normally distributed with a population mean of 6% and a population standard deviation of 18%. … B) What is the probability of a -2.0% or lower average return over a four-year period? So, I understand the basic methodology behind solving this problem. The issue I’m having is with the calculation of the z-statistic. On my first pass on the question I calculated the z-statistic as follows: (o represents the std. deviation) z = Xbar - u / o However, when I checked the solution to problem, the z-statistic was calculated as follows: z = Xbar - u / (o / SQRT(n) ) Could someone please explain to me why the extra divisor of SQRT(n) was thrown in there? Thank you in advance for the help.

thats gotta be wrong. no mention of a sample so we are dealing with population data. I think your way was correct. source of the question?

The question is right out of the CFAI textbook end-of-reading problems, and the solution is out of the back of the book… The SQRT(n) comes in as part of the standard error of a sample mean, but I don’t know why that is being included in this calculation. Help!!

Needs to be included. The issue is the “lower AVERAGE return”. Of course, the answer is wrong anyway because normally we would use a gemoetric average not an arithmetic one but that’s another story…

BTW - Statics is the engineering discipline dealing with loads on things standing still. Statistics is about data analysis.

typo I guess… thanks?