FestEvents is a concert organizer that is evaluating the installation of portable toilets at an outdoor venue where a concert is going to take place. In particular, it is considering an area of the venue that is far away from the existing restrooms. Assume there will be one single queue to access all the portable toilets in this area and that only one person uses a toilet at a time. FestEvents is concerned that if the line is too long, people will find other ways and places to answer nature's call.
FestEvents estimates that there will be 4 arrivals per minute on average to the toilets, with a standard deviation of the time between arrivals of 15 seconds. The average time a person spends using the toilet is 3.12 minutes with standard deviation of 2 minutes.Suppose FestEvents installs 20 portable toilets.
1. On average, what fraction of the toilets will be occupied during the event? (in three decimal point)
2. What is the minimum number of portable toilets that FestEvents must install to ensure that the queue length will not continue to grow without limit (i.e., so that the queue will be stable)? Your answer should be an integer - they can install 2 toilets or 3 toilets but they cannot install 2.6 toilets.