Mathematics 9709 · AS & A Level · The Poisson distribution

The Poisson distribution — practice question

A sports enthusiast produces a magazine every month.
(a(i))[3]

The magazine has, on average, 1 incorrect character in every 540 characters. Use a suitable approximating distribution to determine the probability that a magazine with 2430 characters contains at least 4 incorrect characters.

(a(ii))[1]

Justify the choice of approximating distribution.

(b(i))[1]

The mean monthly number of copies, $X$, of the magazine sold is 123.4. State one condition needed for $X$ to follow a Poisson distribution.

(b(ii))[5]

You are now told that $X$ has a Poisson distribution. Use an appropriate approximating distribution to determine the probability that, in a randomly chosen month, more than 130 copies of the magazine are sold.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Poisson mean estimate: $\bar{\lambda}=\frac{2430}{540}=4.5$

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