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On average, Pierre, an amateur chef, drops 3 pieces of egg shell into every two cake batters he makes. Suppose

that you buy one of his cakes.

a.    In words, define the random variable X.

b.    List the values that Xmay take on.

c.    Give the distribution of X.X~ _____(_____,_____)

d.    On average, how many pieces of egg shell do you expect to be in the cake?

e.    What is the probability that there will not be any pieces of egg shell in the cake?

f.     Let's say that you buy one of Pierre's cakes each week for six weeks. What is the probability that there will not be any egg shell in any of the cakes?

g.    Based upon the average given for Pierre, is it possible for there to be seven pieces of shell in the cake? Why?

  1. X= the number of shell pieces in one cake
  2. 0, 1, 2, 3,...
  3. XP(1.5)
  4. 1.5
  5. 0.2231
  6. 0.0001
  7. Yes


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