I have a long central limit theorem question. I don't know how to do. Can someone please explain and help with the answer? Please see attached image.

Task 2 (Central Limit Theorem) The Central Limite Theorem (CLT) says that the sample mean has the Normal distribution when the sample size is large with some natural conditions. We would like to apply the CLT to approximate some statistical quantities. Let X1, ..., Xn are independent and identically distributed and the average is X = > >!, Xi. Assume that the existance of the expected value and the variance: MX = E[X] E (-0o, co) and ox = Var(X) E (0, co). By the CLT, (X - ux)/Vox -+ Z where Z is a standard Normal random variable as n -+ co. Notice that we can compute the standard Normal cumulative distribution function evaluated at z = 1.96, that is d(z) = P(Z y) = $ with a = 6, S = 3 and n = 40 (Give your answer up to 4 decimal places). QUESTION 10 : Take n = 40 and o? = 1. Using the CLT, approximate the quantile c that the probability P(S, S ci) = 0.025 and the quantile c2 that the probability P(S. > c2) = 0.025. (Give your answer up to 4 decimal places)