Distribution the points in Elliptic curves over a finite field F_p where p is prime.

Question

I want to know why the distribution the points in Elliptic curves over a finite field $\mathbb{F}_p$ where $p$ is prime is uniform. That means the number of points in elliptic curve $E$ with $x$-coordinate in the interval $[0,p/3][p/3,2*p/3][2*p/3,p]$ is roughly equal.