6 Accidents on a particular road occur at a constant average rate of 1 every 4.8 weeks.
- State, in context, one condition for the number of accidents in a given period to be modelled by a Poisson distribution.
Assume now that a Poisson distribution is a suitable model. - Find the probability that exactly 4 accidents will occur during a randomly chosen 12-week period.
- Find the probability that more than 3 accidents will occur during a randomly chosen 10 -week period.
- Use a suitable approximating distribution to find the probability that fewer than 30 accidents will occur during a randomly chosen 2 -year period ( \(104 \frac { 2 } { 7 }\) weeks).