At the emergency department in one of the public hospitals in South East Queensland, patients arrive
according to a Poisson distribution with an average of 15 minutes between arrivals.
i. What is the probability that the hospital experiences a busy period and more than three patients arrive
in half an hour?
ii. Last Saturday, between the hours of 10 am and 12 pm, there were 10 emergency arrivals. A nurse on
shift work was required to triage all emergency arrivals between 9 am and 1 pm that day. How many
patients were expected to arrive over that time?
iii. An on-call doctor is attempting to nap in between emergency arrivals. The doctor is going to set their
alarm such that the probability of a patient arriving in that time is less than 40%. How long can the
doctor set their alarm for?