Poisson approximation to binomial

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

2 questions

Edexcel S2 2005 January Q5
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
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 \(\mathrm { P } ( R \geqslant r ) < 0.01\).