Possible Duplicate:
How to directly compute an integral which corresponds to the normal distribution
Is there any approximate solution for the following definite integral of normal distribution?
$$\int_{a}^{b} e^{-\frac{(x-\mu)^2}{2s^2}} \ dx$$
Possible Duplicate:
How to directly compute an integral which corresponds to the normal distribution
Is there any approximate solution for the following definite integral of normal distribution?
$$\int_{a}^{b} e^{-\frac{(x-\mu)^2}{2s^2}} \ dx$$
You should look into the error function and its approximations
$$\frac{1}{\sqrt{2\pi}\sigma}\int_a^b e^{\frac{-(x-\mu)^2}{2\sigma^2}}\ dx=\frac{1}{2}\left[\text{erf}\left(\frac{b-\mu}{\sqrt{2}\sigma}\right)-\text{erf}\left(\frac{a-\mu}{\sqrt{2}\sigma}\right)\right]$$