The mean number of people arriving at an emergency department is 4 per hour.

1. [2 marks] Explain what assumptions would have to be true for the distribution of arrivals in an hour to be well modelled by a Poisson distribution.
2. [2 marks] Give one reason why these assumptions might not hold in this setting.
3. [2 marks] The emergency department has enough staff to cope with up to 5 people an hour. Assuming for now that a Poisson distribution is valid, what is the probability that more than 5 people will arrive in an hour? Show your working (this could take the form of an Excel formula or an equation).
4. [1 mark] Would it be reasonable to use a normal approximation in the calculation above?