A perfect die is rolled n times. The sum of all points should follow a multinomial distribution, and the pmf is
So when n=100, how can I find $P(330\leq S_n \leq 380)$? It seems that I should apply the normal approximation of multinomial distribution, but I don't know why the approximation is vaild, neither do I know how to apply it.
As a rule, I need to show how much I know about this problem, so:
I know why, how and when I can approximate the binomial distribution with Poisson or Normal distribution.