4 The number, \(X\), of books received at a charity shop has a constant mean of 5.1 per day.
- State, in context, one condition for \(X\) to be modelled by a Poisson distribution.
Assume now that \(X\) can be modelled by a Poisson distribution. - Find the probability that exactly 10 books are received in a 3-day period.
- Use a suitable approximating distribution to find the probability that more than 180 books are received in a 30-day period.
The number of DVDs received at the same shop is modelled by an independent Poisson distribution with mean 2.5 per day. - Find the probability that the total number of books and DVDs that are received at the shop in 1 day is more than 3 .