# Thread: areas under a normal curve

1. ## areas under a normal curve

Hi;
I need to know the formula for calculating area's under a curve of normal distributions
without tables.

Thanks.

2. ## Re: areas under a normal curve

The area under the standard normal curve, from x= a to x= b, is, as I suspect you knew,
$\frac{1}{\sqrt{2\pi}}\int_a^b e^{\frac{-x^2}{2}}dx$.

If you are asking for a way to find an anti-derivative, and then evaluate at a and b, there is no such way. The anti-derivative cannot be expressed in terms of elementary functions (it can, of course, be expressed in terms of the "Error Function", erf(x), which is defined as that integral). That is why there are tables of the standard normal distribution, which are themselves developed by numerical integration.

3. ## Re: areas under a normal curve

thats all thank you.

4. ## Re: areas under a normal curve

Originally Posted by anthonye
Hi;
I need to know the formula for calculating area's under a curve of normal distributions
without tables.

Thanks.
You can use a CAS calculator to evaluate the area under a normal curve, they are programmed to be able to do numerical integration and so are slightly more accurate than the tables. But HallsofIvy is correct, there is no known way to evaluate a Gaussian-type definite integral, EXCEPT between \displaystyle \begin{align*} -\infty \end{align*} and \displaystyle \begin{align*} \infty \end{align*}, or between 0 and one of the infinities (as it's exactly half the region).

5. ## Re: areas under a normal curve

Ok but if and only if I have an area of exactly mu+ i,2,3... standard deviations it can be calculated
because the area are clearly defined.

Nope

7. ## Re: areas under a normal curve

Originally Posted by anthonye
Ok but if and only if I have an area of exactly mu+ i,2,3... standard deviations it can be calculated
because the area are clearly defined.
??? All areas are "clearly defined". If you mean "an integer multiple of the standard deviation", those are sometimes tabulated separately but are still calculated using a numerical integration, as I said, exactly like any other value.

8. ## Re: areas under a normal curve

Ok thanks maybe a bit advanced for me at the moment,This is what I'm on about.

9. ## Re: areas under a normal curve

Those are still only approximations.

10. ## Re: areas under a normal curve

Ok Thank you.