A-LevelMathematicsProbability and statistics9709/62 · May/June 2022 · Q36 Marks
It is known that 1.8% of children in a certain country have not been vaccinated against measles. A random sample of 200 children in this country is chosen.
- (a)Use a suitable approximating distribution to find the probability that there are fewer than 3 children in the sample who have not been vaccinated against measles.[4]
- (b)Justify your approximating distribution.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [B1] Poisson SOI
- [B1] Mean = 3.6 Can be awarded for N(3.6, ...)
- [M1] e^-3.6(1+3.6 +3.6^2/2) Allow any λ Allow one end error Expression must be seen
- [A1] 0.303 (3 s.f.) If M0 awarded allow SC B1 for 0.303 SC Use of binomial: B1 for answer 0.300 (3 sf)
- [B1] [Binomial with] 200 > 50
- [B1] [200 × 0.018 =] 3.6 < 5 or [p =] 0.018 < 0.1 If BO B0 then SC n large, p small: B1 or n large np < 5: B1 or n > 50 and either np < 5 or p < 0.1: B1
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