De Moivre-Laplace Approximation to the Binomial Plugging u =p,o =p(1-p),we get the following de Moivre-Laplace Approximation to the Binomial. If Sn is a binomial random variable with parameters n and p, n is large,and k,l are nonnegative integers,then P(k≤Sn≤l) ≈中 》-3》 l+1/2-npDe Moivre-Laplace Approximation to the Binomial • Plugging 𝜇 = 𝑝, 𝜎 = 𝑝(1 − 𝑝), we get the following de Moivre-Laplace Approximation to the Binomial. • If 𝑆𝑛 is a binomial random variable with parameters 𝑛 and 𝑝, 𝑛 is large, and 𝑘, 𝑙 are nonnegative integers, then 𝐏 𝑘 ≤ 𝑆𝑛 ≤ 𝑙 ≈ Φ 𝑙 + 1/2 − 𝑛𝑝 𝑛𝑝(1 − 𝑝) − Φ 𝑘 − 1/2 − 𝑛𝑝 𝑛𝑝(1 − 𝑝)