1. A local bank branch employs three tellers who can each help a customer on average in 8 minutes, with a standard deviation of 2 minutes. On average, 18 customers arrive at this bank per hour (in a random fashion). How long would customers have to wait if we do NOT pool the employees? (By "not pooling," we mean we have 3 separate lines forming; one in front of each of the 3 tellers. Assume that a person randomly enters one of the lines - each of the 3 lines takes one-third of the arrivals - and a person does not switch lines after entering a line.)
- Approximately 12 minutes
- Approximately 5 minutes
- Approximately 7 minutes
- Approximately 17 minutes
2. A popular ride at Six Flags has two carts that each take exactly 5 minutes for a round (i.e., thrill seekers get in, ride does its thing, thrill seekers get out) and each cart can take 40 thrill seekers (assume that it is always full). You can assume that each seat in a cart is a “server”, or m = 80. Per hour, on average 925 thrill seekers are attracted to this popular ride, who arrive at completely random times. How many thrill seekers are waiting for this popular ride on average?
- Approximately 2.65 minutes
- Approximately 80 thrill seekers
- Approximately 8 thrill seekers
- Approximately 40 thrill seekers
3. The Krasnapolski is a top-of-the-line hotel in Amsterdam, the Netherlands. Among their many services, they rent bicycles to guests. The bicycle checkout is open 24 hours per day 7 days per week and has 40 bicycles on hand. On average, 8 guests request a bicycle each day, arriving completely randomly at all times of the day during the spring and summer seasons. Guests keep bicycles for four days on average, with a standard deviation of two days. How long does a guest on average have to wait for a bike?
- Approximately 1 day
- Approximately 12 hours
- Approximately 75 minutes
- Approximately 0.63 hours