Poisson approximation to the binomialEdexcel International A Level Further Maths: Mind map

Exam questions on Poisson approximation to the binomial

1. A factory produces light bulbs. Each bulb is independently defective with probability 0.02. A box contains 200 bulbs, and $X$ is the number of defective bulbs in a box, so $X\sim B(200,0.02)$.
   Use a Poisson approximation to find the probability that a box contains more than 5 defective bulbs.2 marks
2. An airline finds that each passenger booked on a flight independently fails to turn up with probability 0.03. A flight has 120 passengers booked, and $X$ is the number who fail to turn up, so $X\sim B(120,0.03)$.
   Use the Poisson approximation to find the probability that at most 2 passengers fail to turn up.2 marks
3. A rare genetic condition affects 1 in 500 newborn babies, independently of one another. In one year a region has 1000 births, and $X$ is the number of those babies born with the condition.
   State the exact distribution of $X$, name a suitable approximating distribution, and give a reason why the approximation is suitable.3 marks