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The Jelly Belly Candy Company sells small bags of Jelly Beans

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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 putsXJelly Beans in a bag, whereXhas the following probability distribution.

x P(X = x)

1. 48 0.2

2. 49 0.1

3. 50 0.2

4. 51 0.2

5. 52 0.3

1. (a) Find both theExpected ValueandStandard Deviationof X.

2. (b) The number of jelly beans in any one bag isindependentof the number in any other bags.

   Suppose we count thetotalnumber of jelly beans that the machine puts into the next 100 bags. Denote this number of Jelly Beans byS. Find both theExpected ValueandStandard DeviationofS.

3. (c) What is the probability that the machine will dispense5000 or fewerjelly beans into the 100 bags? In other words P(S=5000) = ?