Normal model of bottle volumes: probability of rejection, expected number rejected and a conditional probability

Normal model of bottle volumes: probability of rejection, expected number rejected and a conditional probability

6 marks

A machine fills bottles with a drink. The volume of drink in a bottle is \(V\) millilitres, where \(V\sim\mathrm{N}\left(750,\ 4.2^2\right)\). Any bottle containing less than \(742\) millilitres is rejected.

  1. Calculate the probability that a randomly chosen bottle is rejected.[2]
  2. A random sample of \(250\) bottles is taken. Estimate how many of these bottles are rejected.[1]
  3. A bottle is chosen at random and is found not to be rejected. Calculate the chance that this bottle holds more than \(756\) millilitres.[3]

Solution:

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Answer:(a) \(0.0284\) (b) \(7\) (c) \(0.0788\)

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