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? |