What is the probability that returns would be less than or equal to 1 standard deviation below the mean?
You can’t use the BAII for this.
50% of the returns will be greater than or equal to the mean, about 34.13% will be between the mean and 1 standard deviation below the mean. So the probability will be `1 - 0.3413 - 0.5 = 0.1586. Note that this is equal to 0.0013 + 0.0214 + .1359 (the left 3 segments of the graph below)
It’s one of the ones you’re supposed to know.
The others are 10%, 5%, and 1% (all for 2 tails).
don’t CFAI provide a Z table in the exam? assuming they do, you only need to know how to use the table to solve problems.
at z = 1.00, a Z-table gives Pr(Z <= z) = .8413, and you readily get the answer 1 - .8413 = .1587
technically, you can use a BA-II for this, but you need to use Calculus.
edit 2: you could also use approximation methods like Simpsons to find the integral from 0 to 1. The more summation terms, the more accurate the result.