4. Jean catches a bus to work every morning. According to the timetable the bus is due at 8 a.m., but Jean knows that the bus can arrive at a random time between five minutes early and 9 minutes late. The random variable \(X\) represents the time, in minutes, after 7.55 a.m. when the bus arrives.
- Suggest a suitable model for the distribution of \(X\) and specify it fully.
- Calculate the mean time of arrival of the bus.
- Find the cumulative distribution function of \(X\).
Jean will be late for work if the bus arrives after 8.05 a.m.
- Find the probability that Jean is late for work.