Data show that, on average, 6.9 patients arrive at the emergency room of a large hospital each hour. In that hospital, Doctors at the emergency room work four hours as a shift.
(a) Determine the mean and variance of the number of patients that a doctor has during a shift.
(b) Find the probability that
i) exactly five patients will arrive at the emergency room during a one-hour period.
ii) within 27 to 29 patients will arrive at the emergency room during a doctor’s shift.
iii) at most two patients will arrive the emergency room during the last hour in a doctor’s shift. Is it unusual?