All international arrivals into a country are placed in hotel quarantine. Outbreaks from hotel quarantine occur at a rate of 2 per month. a. [2 marks] Explain what assumptions would have to be true for the distribution of number of outbreaks in a month to be well modelled by a Poisson distribution? b. [2 marks] Give one reason why these assumptions might not hold in this setting. c. [2 marks] Contact tracing teams have enough staff to cope with up to 3 outbreaks in a month. Assuming for now that a Poisson distribution is valid, what is the probability that more than 3 outbreaks will occur in a month? Show your working (this could take the form of an Excel formula or an equation). d. [1 mark] Would it be reasonable to use a normal approximation in the calculation above?