Moivre-Laplace theorem

The above interpretation is the Lindberg-Levy version of the central limit theorem. The [N np, npq)] normal distribution could also be interpreted as the limiting case of the B n, p) binomial distribution (De Moivre-Laplace theorem), but that is only a special case of the general theorem phrased for sums when the limiting distribution in general is N( /t, na ) normal. 

Normal approximation (De Moivre-Laplace limit theorem). It follows from the interpretation as well as from the central limit theorem that for large enough values of npq (npq > 6 suffices already) the binomial distribution can be approximated by a normal distribution with expected value p = p and variance [Pg.416]

---