CAIE A-Level Mathematics 5.5.3 Normal Approximation to the Binomial

CAIE A-Level Mathematics 5.5.3 Normal Approximation to the Binomial
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise checking whether a binomial variable can be approximated normally, using mean np and variance npq and applying continuity corrections to integer boundaries.

How this is tested

  • verify that both np and nq exceed 5 before replacing B(n, p) by N(np, npq)
  • convert strict or inclusive integer bounds to half-unit boundaries for continuity correction
  • standardise each corrected bound with mean np and deviation √(npq), then combine Φ areas

Question 5(b)

[Maximum number: 5]

On any given day, Cooper either wears a blue jumper or he wears a green jumper or he does not wear a jumper. The probability that he wears a blue jumper is 0.6 and the probability that he wears a green jumper is 0.3 . Whether Cooper wears a jumper of either colour, or does not wear a jumper, on any day is independent of his choice on any other day.

Use a suitable approximation to find the probability that, in any 150-day period, Cooper does not wear a jumper on fewer than 22 days.