Choosing between two normally distributed journey times, an unknown mean from a percentage, and binomial probabilities over several days

A student cycles to school by either the canal path or the main road. On the canal path, the journey time is normally distributed with mean \(33\) minutes and standard deviation \(5\) minutes. On the main road, the journey time is normally distributed with mean \(\mu\) minutes and standard deviation \(4\) minutes.

1. Find the probability that a journey on the canal path takes longer than \(40\) minutes.[2]
2. On the main road, the probability that the journey takes less than \(40\) minutes is \(0.93\). Find the value of \(\mu\).[3]
3. The student leaves home at 07:20 and must reach school before 08:00.
   1. State which way the student should cycle.
   2. Give a reason for your answer.[3]
4. On six school days, the student leaves home at 07:20 and cycles along the main road. The journey times on different days are independent. Find the probability that the student reaches school before 08:00
   1. on all six days;
   2. on at least four of the six days.[5]