Mathematics 9709 · AS & A Level · The Poisson distribution

The Poisson distribution — practice question

A particular data-entry company’s output always contains a small number of wrong characters that appear randomly. Let the proportion of wrong characters be written as $p$, and past evidence shows that $p = 0.0001$. One data set from the company has 14500 characters, with $X$ of these being incorrect.
(a)[3]

Select a suitable approximating distribution and determine $P(X < 4)$.

(b)[3]

The firm's management wants to reduce the value of $p$ by training its employees. Their target is that, for a data set containing 14500 characters, the value of $P(X = 0)$ for the new value of $p$ should be double the value of $P(X = 0)$ when $p = 0.0001$. Use a suitable approximating distribution to find the revised 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 value $\lambda=1.45$

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