Monthly returns for a portfolio of stocks are distrbuted witha 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%
What formula must I use to answer this question? Correct answer is B.
Chebyshev’s Inequality = 1-(1/k^2) for k > 1
2.5 is 2 standard deviations from the mean.
1-1/2^2 = 1-0.25=0.75
i think the correct answer is C.
its actually 96 percent if you consider normal distribution.
Why would 2.5 be 2 standard deviations from the mean?
It isn’t C.
They don’t (at least the OP didn’t) mention the returns being normally distributed, so 75% is correct when using Chebyshev’s inequality.
The question says at least what probability is contained within 2 sigma… At a minimum, we know 75% of the observations fall within 2 standard deviations of the mean according to Chebyshev’s inequality.
Because the mean is 0.5%, when you add two standard deviations (2 * 1%) the upperbound is 2.5%.
Because the mean is 0.5, and the standard deviation is 1.0.
Thus 0.5 + (2* 1.0) = 2.5.
No one here standardizes values anymore? (2.5-.5)/1 = 2 and (-1.5-0.5)/1 = -2. Same results, obviously, but this was the more intuitive way for me 
Thanks!
Good luck Saturday on the exam!