I must not be late on monday mornings again

According to the school rules, a student who arrives at school after 740 on Tuesdays to Fridays and 0950 on Mondays is considered late.


During the school term, Hong Rui will wake up one hour before the late time. He leaves his house exactly half an hour after he wakes up, and walks to Buangkok Mrt Station. The walking time, T, follows a normal distribution of with mean 5 minutes and variance 2 minutes.

Upon reaching Buangkok MRT station, Hong Rui takes the train from Buangkok to Serangoon. The journey takes 7 minutes, while the waiting time, X, follows a normal distribution with mean 4 minutes and variance 2 minutes

At Serangoon MRT station, Hong Rui takes 1 minute to walk from the NEL side of the station to the CCL side. After that, he will then take the train from Serangoon to Marymount station. The journey time is 7 minutes, while the waiting time, Y, follows a normal distribution with mean 4 minutes and variance 3 minutes

After alighting at Marymount station, Hong Rui takes Z amount of time to walk to RJ, where Z follows a normal distribution with mean 4 minutes and variance 2 minutes.

Supposing all the journey times are independent of one another, find the latest time Hong Rui has to wake up on Monday such that the probability of him being late for school is less than 0.05

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Today, I missed the train at Buangkok station and waited for 6 minutes. When I reached Serangoon, the train just left and I had to wait for another 7 minutes T_T