While doing laundry, it seems that each student spends between 3 to 15 minutes in the laundry room per week, and the distribution for each student is assumed to be Uniform on this interval.
a. How long is each student expected to be in the laundry room?
b. What is the variance of the time a student spends in the laundry room?
c. Given that a student has already been in the laundry room for 7 minutes, how long is the student's expected total stay?
d. During a seven day week, in a dorm with 1000 students who each do laundry once, how many minutes do we expect the students to spend altogether in the laundry room (i.e., what is the expected value of the sum of times, with the sum over all 1000 students).
e. What is the approximate probability that, among the 1000 students, the average time spent in the laundry room (per student) exceeds 9.1 minutes during a week? Assume that the students' times are independent.