- Every morning Navtej travels from home to work. Navtej leaves home at a random time between 08:00 and 08:15
- It always takes Navtej 3 minutes to walk to the bus stop
- Buses run every 15 minutes and Navtej catches the first bus that arrives
- Once Navtej has caught the bus it always takes a further 29 minutes for Navtej to reach work
The total time, \(T\) minutes, for Navtej's journey from home to work is modelled by a continuous uniform distribution over the interval \([ \alpha , \beta ]\)
- Show that \(\alpha = 32\)
- Show that \(\beta = 47\)
- State fully the probability density function for this distribution.
- Find the value of
- \(\mathrm { E } ( T )\)
- \(\operatorname { Var } ( T )\)
- Find the probability that the time for Navtej's journey is within 5 minutes of 35 minutes.