5. Vehicles pass a particular point on a road at a rate of 51 vehicles per hour.
- Give two reasons to support the use of the Poisson distribution as a suitable model for the number of vehicles passing this point.
Find the probability that in any randomly selected 10 minute interval
- exactly 6 cars pass this point,
- at least 9 cars pass this point.
After the introduction of a roundabout some distance away from this point it is suggested that the number of vehicles passing it has decreased. During a randomly selected 10 minute interval 4 vehicles pass the point.
- Test, at the \(5 \%\) level of significance, whether or not there is evidence to support the suggestion that the number of vehicles has decreased. State your hypotheses clearly.
(6)