The i-th digit Xi, in the binary expansion of a randomly chosen number in the interval [0, l] is a Bernoulli (0.5) random variable and X1, X2, . . . is a sequence of iid random variables. (a) (3 marks) Use the Central Limit Theorem to approximate the probability that a randomly chosen number in the [0, 1] interval has more than 128 zeros in the rst 512 digits of its binary expansion. (b) (2 marks) Use the De MoivreLaplace Formula to approximate the probability of the event mentioned in part (a)