Z tables for normal distributions

breadmonkey

I'm trying to understand how the values in the so called "Z tables" are derived and I seem completely unable to get the information I need by googling.

Wikipedia tells me that every normally distributed curve is the exponent of a quadratic...

f(x) = e ^ ( ax^2 + bx + c )

...and goes on to define a, b and c in terms of the mean and the standard deviation.

Am I on the right track here? If so, then the value that comes out of the Z table is effectively the area under the curve between 0 and a given value of x? This can be determined by integrating the function and evaluating as appropriate? Can anyone link me to something that shows me what the analytical expression for the integral is? There's no way I'd be capable of working it out myself!

Thanks

Yakuza

The values are normally presented in a form of the integral from minus infinity to x
(e.g. a z-value of 1.96 represents 97.5% of area under the curve)

Here's a tutorial with some background info:
http://stattrek.com/probability-distributions/normal.aspx

A z-value or p-value calculator from the same site:
http://stattrek.com/online-calculator/normal.aspx

Integrating the function is very difficult, it needs numerical methods from what I understand. The tables prevent you from having to do so!