Standardization 1 point possible (graded) Let X1, X2, ..., Xn be i.i.d. random variables with mean / and variance of. Denote the sample mean by Xn = EL Xi n Assume that n is large enough that the central limit theorem (clt) holds. Find a random variable Z with approximate distribution N (0, 1), in terms of Xn, n,/ and o. (Note that / and o' refers to the mean and variance of Xi, not Xn.) (Type barX_n for Xn, mu for u and sigma for . Refer to the standard notation button below.) Z ~ N (0, 1) for Z = ? STANDARD NOTATIONTransformation and Symmetry 1 point possible (graded) Let X N N (2, 2) , i.e. X is a Gaussian variable with mean p, = 2 and variance 02 = 2. Let :1: > 0. Write P (X Z x) in terms of the cdf '1' of the standard Gaussian variable with a positive argument. In other wordsr your answer be in terms of of 'I' (g (33)) , where g (3:) is a function of :8 which takes only positive values for :1: > O. (For example, if your answer is 1 + 'I' (x), type 1+Phi(sqr~t(5)*x).) P(X>:c)=