Use a binomial defect model for expectation, exact and cumulative probabilities.

Use a binomial defect model for expectation, exact and cumulative probabilities.

6 marks
ProbabilityQuestionBank.pdf

A factory makes calculators. Over a long period, 2% of them are found to be faulty. A random sample of 100 calculators is tested.

  1. Write down the expected number of faulty calculators in the sample.
  2. Find the probability that three calculators are faulty.
  3. Find the probability that more than one calculator is faulty.

[6]

Solution:

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Answer:Let \(X\sim\operatorname{Bin}(100,0.02)\). Then \(E(X)=2\), \(P(X=3)=0.1823\), and \(P(X>1)=0.5967\).

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