n standard deviations from mean is ?% of population

• Sep 26th 2012, 10:15 AM
JungleMath
n standard deviations from mean is ?% of population
Please do not provide an answer, please provide a description of the method used.... thank you

What percentage of a population is enclosed if I use 3.359 standard deviations from the mean?

How do I calculate this?
• Sep 27th 2012, 01:07 AM
chiro
Re: n standard deviations from mean is ?% of population
You need to assume a distribution, and I'm going to assume you mean a Normal distribution (but not everything has a Normal distribution just to point this out).

The normal distribution N(0,1) has the PDF of f(x) = [1/SQRT(2*pi)] * e^(-x^2/2) and probability of P(Z < a) = Integral of f(x)dx from -infinity to a.

So based on these hints, what can you say about the probability (i.e. percentage) given this information?
• Sep 27th 2012, 02:27 PM
JungleMath
Re: n standard deviations from mean is ?% of population
Yes, I am assuming normal distribution. However I am still unsure as to how I use the probability density function to find the percentage of a population enclosed if I am 3.6 SDs away from mean... Still working through it in my head though. Will use this info to do more research. Thanks.
• Sep 27th 2012, 02:32 PM
MathoMan
Re: n standard deviations from mean is ?% of population
hint: Probability is the area between the density function graph (Gauss bell) and x-axis.