5. (20 points) A box contains 1000 balls, of which 3 are black and the rest are white. 1000 draws with replacement are made. (a) (6 points) What is the exact value of the probability that precisely 3 of the 1000 draws result in black balls? (b) (6 points) Which is better to use to estimate the value in part (a): the normal approximation or the Poisson approximation? (b) (7 points) Use the appropriate approximation to estimate the value in part (a)