Imagine a student can commute from home to their university by bus where the waiting time for the bus is normally distributed w/ mean of 5 minutes and sd of 1. When leaving campus and heading back home, 75% of the time the student heads back in the afternoon with the wait time distributed as a normal rv with mean 8 and sd 2. 25% of the time the student takes the night bus home with wait time mean of 12 and sd 4. All wait times are independent.

a) What is the expected daily total wait time to campus and back home?

b) What is the variance of the daily commuting time?

c) What is the probability the total wait time for a commute is less than 15 minutes?