Consider a new hotel deciding on cleaning staff hiring for theupcoming season. Cleaning times depend on whether it is a stay-overroom or a check-out. Suppose that a guest will check-out on a givenday with probability 40%. From your experience in similar hotelsyou estimate that a stay-over room cleaning time is well-describedwith normal distribution with average 15 minutes and standarddeviation 1 minute. Check-out room cleaning time is also normal butwith average 30 minutes and standard deviation 10 minutes.
i. Consider an occupied room (stay-over or check-out), what isthe average cleaning time for such a room?
ii. Find the variance for the cleaning time for an occupiedroom.
iii. Suppose that the hotel has 200 rooms, and you estimate thaton a given day a room will be occupied with probability 90%. Onlyoccupied rooms need cleaning. Find the average total cleaning timefor the hotel. iv. Find the variance of the total cleaning time forthe hotel.
Hints: remember var(X) = EX^2 − (EX)^2 .
