### CFA Practice Question

There are 410 practice questions for this study session.

### CFA Practice Question

An investment has a mean return of 15% with a standard deviation of 4.5%. You expect that 75% of the rates will fall within which values?
A. 5.9%; 24.9%
B. 6.0%; 24.0%
C. 6.2%; 24.0%
Explanation: 75% corresponds to k=2 because 0.75 = 1 - 1/22. Therefore, the extremes for the interval are 15% +- 2 * (4.5%) or 6% and 24% (Chebyshev's Inequality).

User Comment
seanny00 When would you use Chebyshev's inequality vs. a z-value? The z value gives you a different result in this case.
Peter you can use the z value only if you're sure that the distribution is normal. in this case there is no mention of that so you have to use the Ch. inequality.
surob or if N>=30
kellyyang yes! this is very tricky question. I don't understand either why needs to use Chebyshev's ? Does anyone knows why?
bhavini thanks Peter. I was getting confused why they were not using z table here.
showmethemoney Ch inequality applies to any distribution
jonan203 @kelly

if, for example, the question asked for what % of rates fall 1.4 deviations from the mean you would use c-inequality as follows:

1 - (1/1.4^2) = 48.98%
tmeeker When in doubt, verify if the answers make sense. B is the only answer that makes sense:
A. 15 +/- X = 5.9 or 24.9 (range is + 9.9 but - 9.1)
B. 15 +/- X = 6 or 24 (range is +/- 9)
C. 15 +/- X = 6.2 or 24 (range is + 9 but - 8.8)

If there is no skew mentioned, the range should be the same in each direction: B.
sloriot I thought we had to multiply with standard error.. not just standard deviation in order to get the conficence interval