Question 2: (8) The Quality Control Manager at Moddies Cola approaches you with a concern about the seal on the caps of their cola bottles. Some of the seals on the bottles can fail, causing the gas to leak out and the Cola to become flat. This happens consistently with 2% of the bottles that they manufacture. (3) a) Your client asks you if you think the above represents a specific type of distribution. Explain the type of distribution to your client and substantiate your answer. b) If you were to sample 200 cola bottles, how many would you expect to have a defective seal, and what would the standard deviation be? (2) c) The Quality Control Manager informs you that their main customer has informed them that they will start penalising Moddies Cola if more than 3% of the Cola bottles they supply have a defective seal. Should Moddies Cola be concerned about this? Discuss in terms of the probability of Moddies Cola receiving a fine. (3)

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