CAIE A-Level Mathematics 6.1.5 Normal Approximation to the Poisson

CAIE A-Level Mathematics 6.1.5 Normal Approximation to the Poisson
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise approximating Po(λ) by N(λ, λ) when the mean is large, applying half-unit continuity corrections and standardising with standard deviation √λ.

How this is tested

  • justify the approximation by showing that the Poisson mean is sufficiently large
  • replace Po(λ) by N(λ, λ) and apply a half-unit correction to every integer boundary
  • standardise with √λ and use the appropriate Φ interval or complementary tail

Question 1(c)

[Maximum number: 4]

The number, X, of used computers donated to a charity has a constant average rate of 2.4 computers per week.

Use a suitable approximating distribution to calculate the probability that more than 50 computers are donated during a 20-week period.