Standard Poisson approximation to binomial

Questions that ask to use Poisson approximation to approximate a binomial distribution B(n,p) where n is large and p is small, with straightforward probability calculations.

4 questions · Moderate -0.3

5.02i Poisson distribution: random events model
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CAIE S2 2020 March Q1
3 marks Moderate -0.3
1 The booklets produced by a certain publisher contain, on average, 1 incorrect letter per 30000 letters, and these errors occur randomly. A randomly chosen booklet from this publisher contains 12500 letters. Use a suitable approximating distribution to find the probability that this booklet contains at least 2 errors.
CAIE S2 2020 November Q1
3 marks Moderate -0.5
1 On average, 1 in 50000 people have a certain gene.
Use a suitable approximating distribution to find the probability that more than 2 people in a random sample of 150000 have the gene.
CAIE S2 2013 November Q1
4 marks Moderate -0.3
1 Each computer made in a factory contains 1000 components. On average, 1 in 30000 of these components is defective. Use a suitable approximate distribution to find the probability that a randomly chosen computer contains at least 1 faulty component.
OCR MEI Further Statistics A AS 2019 June Q2
9 marks Moderate -0.3
2 Almost all plants of a particular species have red flowers. However on average 1 in every 1500 plants of this species have white flowers. A random sample of 2000 plants of this species is selected. The random variable \(X\) represents the number of plants in the sample that have white flowers.
  1. Name two distributions which could be used to model the distribution of \(X\), stating the parameters of each of these distributions. You may use either of the distributions you have named in the rest of this question.
  2. Calculate each of the following.
    Calculate the probability that there are at least 10 plants in the sample that have white flowers.