Question: You are throwing a party and fill a bowl with 63 ounces of punch. Suppose the expected size of each cup of punch is 2 ounces and the standard deviation of the size of a cup of punch is A ounce and each cup is poured independently. You want to know the probability that the bowl will not be empty after 36 cups have been poured.
a. Use Chebyshev's inequality to calculate an upper limit of this probability.
b. You are not satisfied with knowing an upper limit and would like a closer approximation of the probability that the bowl will not be empty. What distribution does the Central Limit Theorem suggest would approximate the probability distribution of the number of ounces needed for 36 cups? Use this distribution to calculate the probability the bowl will not be empty.