Let X1, ... , Xn be i.i.d. r.v.'s with (?nite) unknown mean m and (?nite) known variance s 2, and suppose that n is large.

i) Use the CLT to construct a con?dence interval for m with approximate con?dence coef?cient 1 - a;

ii) What does this interval become if n = 100, s = 1 and a = 0.05?

iii) Refer to part (i) and determine n so that the length of the con?dence interval is 0.1, provided s = 1 and a = 0.05.