A city needs to perform some road maintenance and will rent excavator machines from a company. Each excavator will work at least 1 hour, but no more than 4 hours at a time. It is known that the working time of each excavator is evenly distributed.
a) What is the distribution of one excavator's working time?
b) What is the probability that an excavator works more than 3.5 hours?
c) Given that an excavator has already worked for 2.5 hours, what's the probability that it works at least 1 more hour until it is given a rest?
d) What amount of time represents the highest 30% of excavator working time?
e) The rental fee of each excavator is 200 dollars per hour, if the city rents 3 excavators, what is the expected rental fee per day?