Normal Approximation Based on CLT Given Sn=X1+...+Xn,where the Xi's are i.i.d.random variables with mean u and variance o2.If n is large,the probability P(Sn<c)can be approximated by treating Sn as if it were normal,according to the following procedure. . Calculate the mean nu and variance no2. ll.Calculatez (c-nu)/ovn. lll.Use the approximation P(Sn≤c)≈Φ(z):Normal Approximation Based on CLT • Given 𝑆𝑛 = 𝑋1 + ⋯ + 𝑋𝑛, where the 𝑋𝑖 ’s are i.i.d. random variables with mean 𝜇 and variance 𝜎 2 . If 𝑛 is large, the probability P 𝑆𝑛 ≤ 𝑐 can be approximated by treating 𝑆𝑛 as if it were normal, according to the following procedure. I. Calculate the mean 𝑛𝜇 and variance 𝑛𝜎2 . II. Calculate 𝑧 = (𝑐 − 𝑛𝜇)/𝜎 𝑛. III. Use the approximation P 𝑆𝑛 ≤ 𝑐 ≈ Φ 𝑧