Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
In a large document, typing mistakes arise independently at random with a constant average of $0.2$ per page. In that same document, formatting mistakes also arise randomly and at a constant average of $0.3$ per page.
(a)[2]
Find the probability that there are fewer than 3 typing errors across 10 pages chosen at random.
(b)[4]
Use an approximating distribution to determine the probability that there are more than 50 typing errors in 200 pages chosen at random.
(c)[3]
Find the probability that the combined number of typing and formatting errors in 20 pages chosen at random lies between 8 and 11 inclusive.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies Poisson probability $e^{-2}(1+2+\frac{2^2}{2!})$” …