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Problem 2: Gipper's Gummies (3 points) The Jelly Belly Candy Company sells small bags of Jelly Beans. Each bag is filled using a machine that is supposed to put around 50 Jelly Beans in each bag. However, this is not always achieved because the machine is inexact: it puts X Jelly Beans in a bag, where X has the following probability distribution. X P(X = X) 48 0.2 49 0.1 50 0.2 51 0.2 52 0.3 (a) Find both the Expected Value and Standard Deviation of X. (b) The number of jelly beans in any one bag is independent of the number in any other bags. Suppose we count the total number of jelly beans that the machine puts into the next 100 bags. Denote this number of Jelly Beans by S. Find both the Expected Value and Standard Deviation of S. (c) What is the probability that the machine will dispense 5000 or fewer jelly beans into the 100 bags? In other words P(S