Pictures

These pictures give a rough idea of how well (or not well) the normal distribution approximates the binomial distribution for increasing values of $n$. Specifically, we have $n$ going from 1, 2, 3, 4, 5, 10, 20, 30, 40, 50, 100, 200, 300, 400, 500. Note that the $y$-axis does not necessarily intersect the origin and that the range of values of both axes are changing as well.

$n=1$

$n=2$

$n=3$

$n=4$

$n=5$

$n=10$

$n=20$

$n=30$

$n=40$

$n=50$

$n=100$

$n=200$

$n=300$

$n=400$

$n=500$