Are 99% of all observations 3 standard deviations away from the mean or 2.58 standard deviations away?
I read somewhere that 99 percent of observations under a normal distribution will be +/- 3 standard deviations from mean, but the formula for the 99% confidence inverval of a normal distribution is mean+/- 2.58*std dev
Im confused!
Edited 1 time(s). Last edit at Sunday, May 15, 2011 at 11:13AM by adq123.作者: Jolyn 时间: 2011-7-13 15:56
2.58 is the exact number and usually one would say "more than 99% of observations are within 3 sigma of the mean"
Edit: Distributions which have tails as thin as normal are rare as rubies in the real world so 3 sigma is a pretty good real-world number.
Edited 1 time(s). Last edit at Sunday, May 15, 2011 at 12:01PM by JoeyDVivre.作者: ogoluwa 时间: 2011-7-13 15:56
I just came across a problem where they state that 99% of the observations are within the interval 200 and 400. Calculate the standard deviation, given a normal distribution.
Solution:
Mean:
(400+200)/2 = 300
Standard deviation = (400-300)/3
The solution doesn't take 2.58, rather it considers 3 standard deviations.
Which one do we choose on the exam: 2.58 or 3.作者: chetan86 时间: 2011-7-13 15:56
Yeh, I encountered exactly this question a month ago and had the same question. But you can answer that question using 2,58 sigma (as I remember you get closest answer from three choises). I hope there won't be such ambiguities on the exam.作者: JRossSter 时间: 2011-7-13 15:56
Is this a question on an official CFA mock exam, or on one of the third-party exams (Schweser, Stalla, etc.)?
Edited 1 time(s). Last edit at Sunday, May 15, 2011 at 02:31PM by Oyster.作者: dcfox83 时间: 2011-7-13 15:56
I think its Schweser I have seen this recently作者: MonkeyBusiness 时间: 2011-7-13 15:56
Doesn't this have to do with Hypothesis testing where for 2 tail hypothesis with 99%, the factor is 2.58...
Matori Wrote:
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> Doesn't this have to do with Hypothesis testing
> where for 2 tail hypothesis with 99%, the factor
> is 2.58...
>
> Check page 605 for CFAI Vol 1.
Same thing. Under the null hypothesis the test statistic is normal with mean 0.作者: kmf229 时间: 2011-7-13 15:57
in all my reading, it was 2.58, so I think at the exam I'll play it safe by using 2.58作者: amqata 时间: 2011-7-13 15:57
Miss*Yiota Wrote:
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> in all my reading, it was 2.58, so I think at the
> exam I'll play it safe by using 2.58
Thats what I am doing...
I think some 3rd party notes/questions, might be rounding...
