Number of normals N = 619x
(HTML5 canvas support required)

JavaScript has only provided a uniform random variable Math.random() and a normal random number is sometimes a necessary one to have. There is a polar method to simulate normal RV from uniform RV in A First Course of Probability by Sheldon Ross (pp. 464, 6ed):

1. Generate random numbers ${U}_{1}$ and ${U}_{2}$.
2. Set ${V}_{1}=2{U}_{1}-1,{V}_{2}=2{U}_{2}-1,S={V}_{1}^{2}+{V}_{2}^{2}$.
3. If $S<1$, return step 1.
4. Return the independent unit normals $X=\sqrt{\frac{-2logS}{S}}{V}_{1},Y=\sqrt{\frac{-2logS}{S}}{V}_{2}$.

Here is the (almost) equivalent code in JavaScript:

function normal_random(mean, variance) {
if (mean == undefined)
mean = 0.0;
if (variance == undefined)
variance = 1.0;
var V1, V2, S;
do {
var U1 = Math.random();
var U2 = Math.random();
V1 = 2 * U1 - 1;
V2 = 2 * U2 - 1;
S = V1 * V1 + V2 * V2;
} while (S > 1);

X = Math.sqrt(-2 * Math.log(S) / S) * V1;
//Y = Math.sqrt(-2 * Math.log(S) / S) * V2;
X = mean + Math.sqrt(variance) * X;
//Y = mean + Math.sqrt(variance) * Y ;
return X;
}

The following figure is $N=619100000$: