7 Two flatmates work at the same location. One of them takes the bus to work and the other one cycles. Journey times, measured in minutes, are distributed as follows.
- By bus: Normally distributed with mean 23 and standard deviation 6
- By bicycle: Normally distributed with mean 21 and standard deviation 2
You should assume that all journey times are independent.
- One morning the two flatmates set out at the same time. Find the probability that the person who takes the bus arrives before the cyclist.
- Find the probability that the total time taken for 5 bus journeys is less than 2 hours.
- Comment on the assumption that all journey times are independent.
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