Normal distribution curve area?

[Scott S]

Is there a relatively simple algorithm to compute the area in percentage under the curve as represented by a sigma value?
For example;
3 sigma = 99.7
2 sigma = 95
1 sigma = 68.3
Now suppose I wanted to know 2.5 sigma without a table.

 

[Dr. Courtney]

Wolfram Alpha, MMA, Matlab, and other programs are pretty good at definite integrals.

 

[HallsofIvy]

No, there isn't. The standard normal distribution probability that "z< a" is $\frac{1}{\sqrt{2\pi}}\int_{-\inf}^a e^{-\frac{x^2}{2}} dx$. That cannot be integrated in terms of elementary functions so either do a numerical integration or use a table (which was developed by numerical integrations).