# Probability Question

Ran into this question on Schweser mock

Monthly returns for a portfolio of stocks are distributed with a mean of 0.5% and a standard deviation of 1.0%. Based on this information an analyst can most accurately conclude that the probability of returns between -1.5% and +2.5% in any given month is at least:

A) 68%

B) 75%

C) 95%

The explanation says

“Because we do not know the type of probability distribution, we must use Chebyshev’s inequality and can state that 1 - ¼ = 75% of the observations will be within two standard deviations of the mean.”

I dont get it.In the explanation how did they know it was 2 standard deviations from the mean?The question states standard deviation is 1%

0.5 + x = 2.5

0.5 - x = -1.5 so x = 2 ?

it states it in the range “-1.5% and +2.5%”

mean = .05%

sd = 1%

2sd = 1% * 2 = 2%

.05% + 2% = 2.5%

.05% - 2% = -1.5%

The question is also poorly written: it is just as _ accurate _ to say that the probability is at least 68%. It’s less _ precise _, but just as accurate.

I hate it when the question writers try to be clever; they often fail.

Agreed. The actual exam would rarely have a question written this poorly. Usually very black and white for the most part.

I guess the problem is with the question itself.Thanks for the help everyone

My pleasure.