Solon commutes daily from his home to school. On the average, the trip takes 84 minutes, with a standard deviation of 12 minutes. Assume that the travel time is normally distributed. He leaves his house at 7:45 am.

a. If his next class has a quiz from 9:00 am to 9:10 am, what is the probability that he will only arrive in class at some point during the quiz?

b. How long will his travel time be in the longest 5% of trips?

c. Suppose that he has meetings at 9:15 am for the next four days. Find the probability that he will be late in at least two of these meetings.