### 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 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!!!