# 99% Confidence Interval

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!

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.

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.

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.

Is this a question on an official CFA mock exam, or on one of the third-party exams (Schweser, Stalla, etc.)?

I think its Schweser I have seen this recently

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.

Matori Wrote: ------------------------------------------------------- > 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.

in all my reading, it was 2.58, so I think at the exam I’ll play it safe by using 2.58

Miss*Yiota Wrote: ------------------------------------------------------- > 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… All I know is that 99% = 2.58 in my mind.