The paper talks about the Management science Assignment-Poisson probability distribution. So,develop a forecast for the next month using a four-month moving average method.

## Management science Assignment-Poisson probability distribution

Assume that for a gas and car wash station one car can be serviced at a time. The arrivals follow a Poisson probability distribution, with an arrival rate of 1 car every 10 minutes and the service times follow an exponential probability distribution, with a service rate of 8 cars per hour. 1.What is the probability that the station will be idle? 2.What is the average number of cars that will be waiting for service? 3.What is the average time a car will be waiting for service? 4.What is the average time a car will be at the gas and wash station? Given the following Operating Characteristics from a queuing model with time units specified in hours, answer the five questions: Po = 0.4000 Lq = 0.9000 L = 1.5000 Wq = 0.2000 W = 0.3000 Pw = 0.6000

#### Management science Assignment-Poisson probability distribution

1.What is the average time, in minutes, a customer waits in line before being served? 2.What is the average time, in minutes, a customer spends waiting and being served? 3.What is the average number of customers in the system? 4.What is the probability that there are no customers in the system? 5.If the system serves a customer every 4 minutes, what is the service rate? Consider the following set of time series sales data for a growing company over the past 8 months: Month sales 1 15 2 13 3 18 4 22 5 20 6 23 7 22 8 21 1.Construct a time series plot. What type of pattern exists? 2.Develop a forecast for the next month using the averaging method. 3.Develop a forecast for the next month using the naïve last-value method. 4.Develop a forecast for the next month using a four-month moving average method.

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