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**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.

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**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? |