3. The random variable \(X\) is the number of misprints per page in the first draft of a novel.
- 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
- a randomly chosen page has no misprints,
- the total number of misprints on 2 randomly chosen pages is more than 7 .
The first chapter contains 20 pages.
- Using a suitable approximation find, to 2 decimal places, the probability that the chapter will contain less than 40 misprints.