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Calculus/Standard Deviation & Confidence Intervals

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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.

Thanks in advance

Answer
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
http://www.youtube.com/watch?v=u_ZWaxseuio

Abe

Calculus

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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

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