CFA Practice Question

CFA Practice Question

A variable, W, is normally distributed with a mean of 12. 68% of its observations lie between 8 and 16. The coefficient of variation of W is ______.
A. 3.0
B. 0.33
C. 0.66
Explanation: For a normal distribution, 68% of the observations lie within one standard deviation of the mean. Hence, the standard deviation of X equals 12-8 = 4. The coefficient of variation is then equal to standard deviation/mean = 4/12 = 0.33.

User Contributed Comments 17

User Comment
Rivermax using the formula for the mean a+b/2

8+16 / 2 = 12

=> normal distribution mean- lower range = 12 - 8 = 4

coefficient of cariance = sd/mean = 4/12 = 0.33
JHeld Wow, i read this as 12.68% of all observations lie between 8-16...time for bed!
StanleyMo same as me, lol.
Yohan3109 I thing that in a normal distribution they have 3 standard deviation in each side of the mean.
so exemple 12,68 - 16 =3,32 I think that a standard deviation equal 3,32 / 3 = 1,107
why is 4...
thammy JHeld and StanleyMo, I did the same too! And I thought I was going nuts.
kellyyang Jheld: I read same as you 12.68%. of couse got wrong for this one.
boddunah i took mean as 12.68%.i thought question did not make sense. i assumed 1 stan. deviation and got approximate answer. hope they seperate them clearly.
mindi me too! the question did not make any sense to me!!!
Merke Guys, these comments of reading it as 12.68% made my day :)))
Kathkun guys, I cant believe so many of us made that same mistake HAHA!
fmhp I also made the same mistake concerning the value of the mean. I was not told that you have to be a pretty good and careful reader to pass that exam.
simonbenfrech Common sense: otherwise the coefficient of variation would be around 70...
Mikehuynh SD = 4
Mean = 12
Coefficient of variation = SD/mean= 4/12= 0.333
anele1 Also read 12.68% and was completely lost and gave up!!
CalebMast I read 12.68% but guessed because each answer was in a ratio of 1/3 (even .66 is 2*(1/3)). 3 didn't make sense, and .66 seemed a little too much...feels like most of what has to happen with this exam. ("seems too much"). Either way, mean of 12 is huge...
Rsanches Same mistake, read 12.68%....
sunday128 Bloody hell... 12.68% Really?
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