solve these

a) 7 marks] i) [2 marks State the Central Limit theorem in one of the forms given in lectures. ii) [5 marks] Let X1, X2, ..., X48 be i.i.d Uniform (0,1 ) random vari- ables, and set X = 1 Si=48 48 izl Xi. Using the Central Limit Theorem, compute P(X 0.55). Express your answer in terms of the $ function. In your answer include a sketch of a suitable curve with a shaded area corresponding to this probability