- [Maximum mark: 6]
The number of traffic accidents at a road junction is modelled by a Poisson distribution with a mean of 0.76 accidents per week.
(a) Under this model, calculate the probability that
(i) there are at least 2 accidents in a particular week.
(ii) there will be exactly 3 accidents in a particular 4‑week period. [4]
The local traffic authority wishes to determine the probability that, in an 8‑week period, fewer than 2 accidents occur in a week on exactly 5 occasions. It assumes that the weekly occurrence of accidents is independent of the week in which these occur.
(b) State the appropriate model that the traffic authority should use to determine this probability. [2]