Chapter D Group Homework ALL ANSWERS FALL-2021 SOLUTION 100% CORRECT GUARANTEED GRADE A+

Paul Fenster owns and manages a chili-dog and soft-drink stand near the Kean U. campus. While Paul can service 30 customers per hour on the average (μ), he gets only 20 customers per hour (λ). Because Paul could wait on 50% more customers than actually visit his stand, it doesn’t make sense to him that he should have any waiting lines. Paul hires you to examine the situation and to determine some characteristics of his queue. After looking into the problem, you find it follows a Poisson distribution and is negatively exponentially distributed. What is/are: a. the number of customers in the system a. 2 b. the time (minutes) that a customer waits before being served? a. 6 c. How busy is the server? a. 66% d. What is the probability that there are more than 5 customers waiting? a. 8.7% 2. A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poison distribution and answer times a exponentiallydistributed. a. Find the probability that the employee is idle. a. 33.3% b. Find the proportion of the time that the employee is busy. a. 66.7% c. Find the average number of people waiting and receiving some information. a. 2 d. Find the average number of people waiting to get some information. a. 1.3 e. Find the average time, in minutes, that a person waits before receiving information. a. .06667(60) = 4.0002 minutes f. Find the average time, in minutes, that a person spends in the system? a. .1(60) = 6 minutes 3. Sue’s Coffee Shop decides to install an automatic coffee vending machine outside one of its stores to reduce the number of people standing in line inside. The coffee shop charges $3.50 per cup. However, it takes too long for people to make change. The service time is a constant 3 minutes, and the arrival rate is 15 per hour (Poisson distributed). a. What is the average wait in line? a. .075 hours or 4.5 minutes b. What is the average number of people in line? a. 1.125 c. Sue raises the price to $5 per cup and takes 30 seconds off the service time. However, because the coffee is now so expensive, the arrival rate drops to 10 per hour. Now what are the average wait time and the average number of people in the queue (waiting)? a. Wait time a. .1488 hours or 8.93 minutes b. People in que a. .0149 hours or .89 minutes