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# Calculus/Standard Deviation & Confidence Intervals

Question
Hi there,

I would really appreciate some help with some concepts in stats that I am having trouble grasping. I cannot understand what is meant by 3 standard deviations from the mean. According to my Introductory Stats unit lecture notes, to get a 99.7% confidence interval, you add 3 standard deviations of the distribution to the mean of the distribution but the z-score corresponding to 99.7% is 2.78.

Hello,

First of all, this is not a calculus question...it is statistics.  Next time, please
post in that section.

For *any* Normal Distribution, the area (i.e. percentage of area) between any two values
(or the area to the right or left of a value) depends only on the number of standard
deviations away from the mean.  So, it does not matter of the mean is 1 or 1000, what
matters is the difference between that mean, the value of interest and the number of standard
deviations away from the mean (a.k.a. z-score).

Check these website for more about it.
http://math.elon.edu/statistics112/norm_dist.html
http://daphne.palomar.edu/stat/wpbetweensame.html

Abe

Calculus

Volunteer

#### Abe Mantell

##### Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

##### Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook