6. Cars arrive at a motorway toll booth at an average rate of 150 per hour.
- Suggest a suitable distribution to model the number of cars arriving at the toll booth, \(X\), per minute.
- State clearly any assumptions you have made by suggesting this model.
Using your model,
- find the probability that in any given minute
- no cars arrive,
- more than 3 cars arrive.
- In any given 4 minute period, find \(m\) such that \(\mathrm { P } ( X > m ) = 0.0487\)
- Using a suitable approximation find the probability that fewer than 15 cars arrive in any given 10 minute period.
January 2011