# Thread: n standard deviations from mean is ?% of population

1. ## n standard deviations from mean is ?% of population

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

How do I calculate this?

2. ## 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?

3. ## 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.

4. ## Re: n standard deviations from mean is ?% of population

hint: Probability is the area between the density function graph (Gauss bell) and x-axis.