Central Limit Theorem

Z = Xi + . . . + Xn, Xi ~ N(0,1) => Z ~ Xn

E(Y)=0 , Var(Y)=1

Portanto,

Y ~ N(0,1)

X <- runif (12*10^5, -1/2, 1/2)
X <- matrix (X, nrow=12)
Y <- apply (X, 2, sum)

Histrograma chi-quadrado

hist (Y, 40, prob=T)
curve (dnorm(x), col='orangered', lwd=3, add=T)