Poisson model and probabilitiesAQA A-Level Further Maths: Mind map

Exam questions on Poisson model and probabilities

1. Faults occur at random, independently and at a constant average rate of 2.5 per metre in a long roll of fabric. The number of faults, $X$, in one metre is modelled by $X\sim\mathrm{Po}(2.5)$.
   Find the probability that a 2 metre length of the fabric contains no faults.2 marks
2. A call centre receives calls at random at a constant average rate of 6 per hour. The number of calls, $Y$, received in one hour is modelled by $Y\sim\mathrm{Po}(6)$.
   The manager notices that calls are much more frequent between 12 noon and 1 pm than at other times of the day. Explain why $\mathrm{Po}(6)$ is not suitable as a model for the number of calls in every hour of the working day.2 marks
3. The number of typing errors on a page of a manuscript is modelled by $X\sim\mathrm{Po}(1.8)$. Errors on different pages occur independently of one another.
   Find $\mathrm{P}(X\ge3)$.3 marks