3. The random variable $X$ is the number of misprints per page in the first draft of a novel.\\
(a) State two conditions under which a Poisson distribution is a suitable model for $X$.

The number of misprints per page has a Poisson distribution with mean 2.5. Find the probability that\\
(b) a randomly chosen page has no misprints,\\
(c) the total number of misprints on 2 randomly chosen pages is more than 7 .

The first chapter contains 20 pages.\\
(d) Using a suitable approximation find, to 2 decimal places, the probability that the chapter will contain less than 40 misprints.

\hfill \mbox{\textit{Edexcel S2  Q3}}