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2010 ACJC P2 Q12 [Modified]

2010 ACJC P2 Q12 [Modified]

11 marks
Prelims

A variety of fish are bred in large batches with \(20\%\) is the fish bred being salmon fish.

  1. Explain why a binomial distribution is appropriate for modelling the number of salmon fish in a catch of \(n\) fish.[1]
  2. What is the probability that the \({{10}^{\mathrm{th}}}\) fish caught is the sixth salmon fish?[2]
  3. A large number, \(n\), of fish is caught.
    1. If the probability of having \(10\) or fewer salmon fish caught is at most \(0.0227\), find the least possible number of fish caught.[5]
    2. Find the possible values of \(n\) such that \(15\) is the most likely number of salmon fish caught.[3]

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Answer:(i) Fixed \(n\), two outcomes, approximately independent trials and constant salmon probability \(0.2\). (ii) \(0.00330\) (iii)(a) \(n=89\) (iii)(b) \(74\leq n\leq79\) (or \(75\leq n\leq78\) if a unique mode is intended)

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