A) If you assume the distribution of income is normally distributed, with mean 45,000 and standard deviation 15,000, what is the family income cutoff (the largest amount of family income that would still qualify someone to receive the welfare program)? B) Why is your answer to A) likely badly incorrect? C) In a random sample of 100 families from the population, what is the probability that the average income is higher than 40,000? Explain why you can use the normal distribution to answer this question, although you know the true distribution of income is not normal. Problem 6: The following is a variant of the coin in box example from the Module 3c lecture. Suppose the box contains four coins: two fair coins in which the probability of a head is .5, one two-sided head coin, and one biased coin where the chances of a head is 2/3. a) You pick a coin at random, flip it and it comes up as a tail. What is the probability that you picked the biased coin? b) You again pick a coin at random and flip it twice. Suppose you get a head on the first toss and tail on the second toss. What is the probability that you picked one of the fair coins? Problem 7: Suppose a random variable is uniformly distributed between 2 and 4. What is the probability that average of 50 random draws from this distribution will exceed 3.1