Question: The number of patients arriving at a hospital’s accident and emergency unit during a peak period on a Saturday night and who require immediate attention has been shown to follow a Poisson distribution with parameter μ = 3. The unit can handle up to four such patients during this period. If more than four patients arrive in this period, the patients in excess of four must be sent to another hospital. The following questions refer to the peak period on Saturdays.

a) On a given Saturday, what is the probability of having to send patients to another hospital?

b) By how much must present facilities be increased to permit handling of all patients arriving on at least 95% of Saturdays?

c) What is the expected number of patients arriving each Saturday?

d) What is the most probable number of patients arriving each Saturday?

e) Give the main assumptions we make when we model the above situation using a Poisson distribution.