Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
A particular data-entry company’s output always contains a few incorrect characters chosen at random. Let the proportion of incorrect characters be denoted by $p$, and past data have shown that $p = 0.0001$. One dataset from the company has 14500 characters, with $X$ of them incorrect.
(a)[3]
Use a suitable approximating distribution to determine $P(X < 4)$.
(b)[3]
The firm's management wants to reduce the value of $p$ by training their employees. Their goal is that, for a data set containing 14500 characters, the value of $P(X = 0)$ for the new value of $p$ should be twice the value of $P(X = 0)$ when $p = 0.0001$. Use a suitable approximating distribution to find the new value of $p$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Mean parameter: $\lambda=1.45$” …