3 A bus runs from point A on the outskirts of a city, stops at point B outside the rail station, and continues to point C in the city centre.
The journey times for the sections A to B and B to C vary according to traffic conditions, and are modelled by independent Normal distributions with means and standard deviations as shown in the table.
| \multirow{2}{*}{} | Journey time (minutes) |
| \cline { 2 - 3 } | Mean | Standard deviation |
| A to B | 21 | 3 |
| B to C | 29 | 4 |
- Find the probability that a randomly chosen journey from A to B takes less than the scheduled time of 23 minutes.
For every journey, the bus stops for 1 minute when it reaches B to drop off and pick up passengers.
- Find the probability that a randomly chosen journey from A to C takes less than the scheduled time of 50 minutes.
Mary travels on the bus from the station at B to her workplace at C every working day. You should assume that times for her bus journeys on different days are independent.
- Find the probability that the total time taken for her five journeys on the bus in a randomly chosen week is at least \(2 \frac { 1 } { 2 }\) hours.
- Comment on the assumption that times on different days are independent.