No, $P(X<1)$ is different from $P(|X|<1)$. After all $-2 < 1$ but $|-2|$ isn't! To get $P(|X|<1)$ you need to find this area: ![required area][1] . . . While $P(X<1)$ would be this area: ![wrong area][2] Credit: I used the `shadenorm` function [here](https://gist.github.com/tony91782/950812), which was written by [Tony Cookson](http://novicemetrics.blogspot.com.au/2011/04/how-to-shade-under-normal-density-in-r.html). It looks like there's a similar function [`shade.norm` in package `asbio`](http://www.inside-r.org/packages/cran/asbio/docs/shade.norm) [1]: https://i.sstatic.net/SaV05.png [2]: https://i.sstatic.net/yZ3l2.png