[terence]

Question 1
Jonathan sells lottery tickets at a small stand in a shopping mall. The average time between two customer arrivals equals 15 minutes (Poisson arrival process). Jonathan can sell tickets to exactly 5 customers per hour. What is the average time a customer will spend in the system (waiting plus service time), expressed in minutes?

Question 2
Consider a fast-food outlet with only one employee. All customers wait in a queue until they are served by the employee. The average time between two customer arrivals equals 3.5 minutes (Poisson arrival process). The average time required by the employee to help a customer equals 2.6 minutes (negative exponentially distributed). What is the average number of customers being served by the employee (or stated differently: what is the expected number of customers who are in the system, but not in the waiting line)?

Question 3
Donna owns a small shop in the city centre, where she sells coffee mugs. Donna is the only person working in this shop. On average, 3 customers enter the shop every hour (Poisson distributed). Donna helps every customer that enters the shop. She can help on average 5 customers per hour (negative exponentially distributed service times). What is the probability that there are 4 customers or less in Donna's shop (waiting plus being served)? Express the probability as a number between 0 and 1.

Question 4
Ramon's Barber Shop has one barber. Customers enter the shop with an average inter-arrival time of 17 minutes (Poisson arrival process). The barber is able to give any haircut in exactly 13 minutes. What is the average waiting time (excluding the time customers are actually having their hair cut), expressed in minutes?

Question 5
The QuickMoney bank has a single Automated Teller Machine (ATM). The time between two arrivals of clients equals on average 4.1 minutes (Poisson arrival process). On average, 28 clients can retrieve money from the ATM per hour (negative exponentially distributed service times). What is the average number of clients at the ATM (waiting plus using ATM)?

Question 6
Consider a paint shop for small steel products, where arriving products are spray painted one by one. On average 73 products arrive per hour at the paint shop (Poisson distributed). Painting of one product requires on average 0.4674 minutes (negative exponentially distributed). What is the probability that there is exactly 1 product in the paint shop (waiting plus being processed)? Express the probability as a number between 0 and 1.

Question 7
The company "New Internet Enterprises" has one internet server. The internet server receives many requests, with an average time between two arriving requests of 0.33 seconds (Poisson arrival process). The internet server can process exactly 352 requests per minute. What is the average number of requests waiting for a response (excluding requests actually being processed)?

Question 8
Amanda assembles computers at her workstation. On average there are 27 computers in the system (waiting plus being assembled by Amanda). Assume that the number of arriving computers is distributed according to a Poisson distribution and that the time Amanda needs for assembling a computer is negative exponentially distributed. What is the probability that the number of computers in the system is less than or equal to 22 at an arbitrary point in time?

Question 9
Currently, a certain process is performed by a machine which has a processing time per product that is exactly equal for each of the products. The time products spend in the waiting line in front of the machine equals 30.5 minutes on average and the total time a product spends at this process (waiting plus processing) equals 41.2 minutes on average. The machine is rather old and the manager considers replacing the machine by a person. He estimates that this person can perform the same task with the same average speed; however, this time will now be distributed according to a negative exponential distribution. Assume that the number of products that arrive at the process is distributed according to a Poisson distribution. What is the expected time a product will spend in the new system with the person replacing the machine (waiting plus processing)? Express your answer in minutes.

Question 10
The "FastScan" consulting company has performed a little investigation at the local grocery store. From this investigation it is apparent that customers arrive at the registers according to a Poisson distribution with an average value of 18 customers per hour. There are 3 registers available with identically skilled employees. There is one common waiting line for the registers. The customer who is waiting longest, goes to the first available register. One employee can help on average 10 customers per hour (negative exponentially distributed service times). What is the average time customers spend in the waiting line (expressed in minutes)?

[terence]

HELP me please T_______T