Compare two normal journey-time models and calculate a mixed-route arrival probability.

A van can take either Route A or Route B for a particular journey. If Route A is taken, the journey time may be assumed to be normally distributed with mean 46 minutes and a standard deviation 10 minutes. If Route B is taken, the journey time may be assumed to be normally distributed with mean µ minutes and standard deviation 12 minutes.

1. For Route A, find the probability that the journey takes more than 60 minutes.[2]
2. For Route B, the probability that the journey takes less than 60 minutes is 0.85. Find the value of µ.[3]
3. The van sets out at 06:00 and needs to arrive before 07:00.[3]
   1. Which route should it take?
   2. Justify your answer.
4. On five consecutive days the van sets out at 06:00 and takes Route B. Find the probability that[5]
   1. it arrives before 07:00 on all five days;
   2. it arrives before 07:00 on at least three days.