3 The number of calls received at an office per 5 minutes is modelled by a Poisson distribution with mean 3.2.
- Find the probability of
(A) exactly one call in a 5 -minute period,
(B) at least 6 calls in a 5 -minute period. - Find the probability of
(A) exactly one call in a 1 -minute period,
(B) exactly one call in each of five successive 1-minute periods. - Use a suitable approximating distribution to find the probability of at most 45 calls in a period of 1 hour.
Two assumptions required for a Poisson distribution to be a suitable model are that calls arrive
- at a uniform average rate,
- independently of each other.
- Comment briefly on the validity of each of these assumptions if the office is
(A) the enquiry department of a bank,
(B) a police emergency control room.