99% Confidence interval and standard deviation

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dtrynoski

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So there a question on the sample exam in the answer which they state that 99% of observations under a normal distribution will be plus/minus three standard deviations. Is this correct? My understanding was that 99% of observations under a normal distribution will be plus/minus 2.58 standard deviations
 
Yes, I remember seeing them both in the text at different locations. (i.e. 3 and 2.58)
I guess both are correct, 3 being more conservative than 2.58. So, if there is a choice between 3 and 2.58, I would choose 3. i.e. if a value lies between +- 2.58 standard deviations, it must for sure lie between +-3 standard deviations too.
Someone, please comment on this.
 
68% values lie in between +- 1 sd
95% of values lie in between +- 2 sd
99% of values lie in between +-3sd
Never heard of using +-2.58sd :S.
 
Maybe the other 2 options are less than +- 2.58?
Which are the 2 other options available to choose from?
 
The textbook mention that +- 3 is an approximate value. Hence to be exact, reading from the z-table.
Since it is 99%f observations under a normal distribution, you shld find 0.995. Taking into consideration one side of the curve, hence alpha = 1% / 2 = 0.5%. (Hence read 1-0.005=0.995 from the table, and you can find it to be 2.58) Best approx.
And its +-3 as it is prob the closest to be.
 
Yes 3 is the approximate value and the CFAI book mentions that. But if there is a choice with 3 and 2.58, i would go with the later.
 
General practice is to say that +-3s. But, 2.58 is technically more correct. It doesn’t matter you can use anyone you want. I would go for +-3s
 
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