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Al Julanda Al Hashmi

Al J.

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Sparagowski \& Associates conducted a study of service times at the drive-up window of fast-food restaurants. The average service time at McDonald's restaurants was $2.78 \mathrm{min}$ utes (The Cincinnati Enquirer, July 9,2000 ). Service times such as these frequently follow an exponential distribution. a. What is the probability that a customer's service time is less than 2 minutes? b. What is the probability that a customer's service time is more than 5 minutes? c. What is the probability that a customer's service time is more than 2.78 minutes?

Essential of Statistics for Business and Economics

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Aishwarya Krishnakumar verified

Numerade educator

The mechanical pony ride machine at the entrance to the City Star Mall provides 2 minutes of riding for OMR 0.250. Children wanting to ride the pony arrive according to a Poisson distribution with a mean rate of 15 per hour. What fraction of the time is the pony idle? What is the average number of children waiting to ride the pony?

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Areen Dabadghav verified

Numerade educator

Retail sales at Samakati seafood supply are handled by one clerk. Customer arrivals are random, and the average arrival rate is 21 customers per hour. A study of the service process shows that the average or mean service time is 2 minutes per customer, with a standard deviation of σ = 1.2 minutes. What are the operating characteristics of this waiting line system?

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Aishwarya Krishnakumar verified

Numerade educator

Boats arrive for fuel and service at a marina docking facility according to a Poisson probability distribution, with a mean of 5 boats per hour. The service times follow an exponential probability distribution, with a mean of 10 boats per hour. Customer waiting time is valued at OMR 40 per hour, and the cost to operate each dock (channel) is OMR 20 per hour. What is the lowest-cost design for the docking facility (i.e. how many service channels should it have)?

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Aishwarya Krishnakumar verified

Numerade educator

A Marina has a docking facility where two boats at a time can stop for gas and servicing simultaneously. Assume that arrivals follow a Poisson probability distribution, with a mean of 5 boats per hour, and that service times follow an exponential probability distribution, with a mean of 7 boats per hour. a. What is the probability that the boat dock will be idle? b. What is the average number of boats that will be waiting for service? c. What is the average time a boat will spend waiting for service? d. What is the average time a boat will spend at the dock? e. If you were the manager of the marina, would you be satisfied with the service level your system will be providing? Why or why not?

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A Marina has a docking facility where one boat at a time can stop for gas and servicing. Assume that arrivals follow a Poisson probability distribution, with a mean of 5 boats per hour, and that service times follow an exponential probability distribution, with a mean of 7 boats per hour. a. Compute the operating characteristics of the customer waiting line. b. If you were the manager of the Marina, would you be satisfied with the service level your system will be providing? Why or why not?

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Danielle Ashley verified

Numerade educator

During the weeknight evenings, customers arrive at a video and DVD rental outlet at the average rate of 1.5 customers per minute. The checkout clerk can serve an average of two customers per minute. Assume Poisson arrivals and exponential service times. a. What is the probability that no customers are in the system? b. What is the average number of customers waiting for service? c. What is the average time a customer waits for service to begin? d. What is the probability that an arriving customer will have to wait for service? e. Do the operating characteristics indicate that the one-clerk checkout system provides an acceptable level of service?

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