Prof. Z has a pretty serious coffee dependency. He randomly needs a coffee fix and there is no relationship between one coffee fix and the next. There is no relationship between his need for coffee and any activity he is performing or the time of the day. You are getting worried so you observe him for a week and determine he consumes 12 cups of coffee every 18 hours he is awake (he sleeps the other 6 hours per day). Based on this answer the following.

a) If he gets up at 7am tomorrow then at what time would you expect that he drinks his first cup of coffee?

b) If he gets up at 7am tomorrow what is the probability he drinks his first cup of coffee, for the next 18 hours, while he is teaching your 1 hour lecture of ECO220 from 11am to 12pm noon?

c) If he gets up at 7am tomorrow what is the probability he drinks either 1 or 2 cups of coffee while teaching all 3 lectures of ECO220 from 11am to 1pm?

d) Using an approximation to the normal distribution, solve for the probability that Prof. Z drinks more than 4200 and less than 4400 cups of coffee in the next 365 days while he is awake (hint: that is the next 6570 hours of being awake)