Question: Five students are waiting to talk to the TA when office hours begin. The TA talks to the students one at a time, starting with

Five students are waiting to talk to the TA when office hours begin. The TA talks to the students one at a time, starting with the first student and ending with the fifth student, with no breaks between students. Suppose that the time taken by the TA to talk to a student has a normal with a mean of 8 minutes and a standard deviation of 2 minutes, and suppose that the times taken by the students are independent of each other.
(a) What is the probability that the total time taken by the TA to talk to all five students is longer than 45 minutes?
(b) Suppose that the time that elapses between when the TA starts talking to the first student, and when the TA starts to have a headache, has a normal with a mean of 28 minutes and a standard deviation of 5 minutes, which is independent of the times taken to talk to the students. What is the probability that the TA's headache starts at a time after the TA has finished talking to the third student?

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