Exercise III. Suppose 500 people audition for admission to a dance school. Each dancer in one half of the group will be admitted with probability 0.071 while each dancer in the other half of the group will be admitted with probability 0.04. Let X be the total number of dancers admitted. [Notice that X is the sum of two binomial variables). (a) Find the mean and variance of X. (b) Use normal approximations to binomial random variables to approximate (i) the probability that more than 30 dancers are admitted. (ii) the probability that at least 20 dancers are admitted