Question 1: Suppose 10 percent of households earn over 80,000 dollars a year,and 0.25 percent of households earn over 450,000. A random sample of 400 households has been chosen. In this sample, let X be the number of households that earn over 80,000, and let Y be the number of households that earn over 450,000.Use normal and Poisson approximation, whichever is appropriate in either case, to find the simplest estimates you can for the probabilities P(X 48) and P(Y 2).

Question 2 :John each day performs the following experiment: he repeatedly flips a coin until he gets tails and counts the number of coin flips needed.

(a) Approximate the probability that in a year there are at least 3 days where he needed more than 10 coin flips.

(b) Approximate the probability that in a year there are more than 50 days where he needed exactly 3 coin flips.