Poisson approximation to binomial

Use Poisson approximation when n is large and p is small (np < 5), typically for rare events.

3 questions · Moderate -0.5

2.04d Normal approximation to binomial
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Edexcel S2 2014 January Q1
8 marks Moderate -0.3
  1. The probability of a leaf cutting successfully taking root is 0.05
Find the probability that, in a batch of 10 randomly selected leaf cuttings, the number taking root will be
    1. exactly 1
    2. more than 2 A second random sample of 160 leaf cuttings is selected.
  2. Using a suitable approximation, estimate the probability of at least 10 leaf cuttings taking root.
Edexcel S2 2005 January Q5
13 marks Moderate -0.3
5. From company records, a manager knows that the probability that a defective article is produced by a particular production line is 0.032 . A random sample of 10 articles is selected from the production line.
  1. Find the probability that exactly 2 of them are defective. On another occasion, a random sample of 100 articles is taken.
  2. Using a suitable approximation, find the probability that fewer than 4 of them are defective. At a later date, a random sample of 1000 is taken.
  3. Using a suitable approximation, find the probability that more than 42 are defective.
    (6)
OCR S2 Q4
7 marks Moderate -0.8
4 DVD players are tested after manufacture. The probability that a randomly chosen DVD player is defective is 0.02 . The number of defective players in a random sample of size 80 is denoted by \(R\).
  1. Use an appropriate approximation to find \(\mathrm { P } ( R \geqslant 2 )\).
  2. Find the smallest value of \(r\) for which \(\mathrm { P } ( R \geqslant r ) < 0.01\).