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- The time between arrivals of buses follows anexponential distribution, with a mean of 60 minutes.a What is the probability that exactly four buses willarrive during the next 2 hours?b That at least two buses will arrive during the next 2hours?c That no buses will arrive during the next 2 hours? d A bus has just arrived. What is the probability thatit will be between 30 and 90 minutes before the next busarrives?An average of 40 jobs per day arrive at a factory. Thetime between arrivals of jobs is exponentially distributed.The factory can process an average of 42 jobs per day, andthe time to process a job is exponentially distributed.a What is the probability that exactly 180 jobs arriveat the factory during a 5-day period?b On the average, how long does it take before a jobis completed (measured from the time the job arrives atthe factory)?c What fraction of the time is the factory idle? d What is the probability that work on a job will be-gin within 2 days of its arrival at the factory?On average, 40 jobs arrive per day at a factory. The time between arrivals of jobs is exponentially distrib-uted. The factory can process an average of 42 jobs per day, and the time to process a job is exponentiallydistributed.a. On average, how long does it take before a job iscompleted (measured from the time the job arrivesat the factory)?b. What fraction of the time is the factory idle?c. What is the probability that work on a job willbegin within two days of its arrival at the factory?
- I ONLY NEED HELP WITH PART C,D,E,F PLEASE. Gubser Welding, Inc., operates a welding service for construction and automotive repair jobs. Assume that the arrival of jobs at the company's office can be described by a Poisson probability distribution with an arrival rate of three jobs per 8-hour day. The time required to complete the jobs follows a normal probability distribution, with a mean time of 2.5 hours and a standard deviation of 1.6 hours. Answer the following questions, assuming that Gubser uses one welder to complete all jobs. (a)What is the mean arrival rate in jobs per hour? (Round your answer to four decimal places.) per hour CORRECT ANSWER IS 0.3750 (b)What is the mean service rate in jobs per hour? (Round your answer to four decimal places.) per hour CORRECT ANSWER IS 0.4000 (c) What is the average number of jobs waiting for service? (Round your answer to four decimal places.) 8.12563 IS WRONG (d) What is the average time (in hours) a job waits before…The emergency room of the community hospital in Farmburghas one receptionist, one doctor, and one nurse. The emergency room opens at time zero, and patients begin to arrive at a certain time later. Patients arrive at the emergency room according to the following probability distribution:Suppose I arrive at an M/M/7/FCFS/8/∞ queuing systemwhen all servers are busy. What is the probability that I willcomplete service before at least one of the seven customersin service?
- A fast-food franchise is considering operating a drive-up window food- service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercomstation at the back of the parking lot and then drive to the service window to pay for and receive their orders. Consider a two-channel operation with two service windows and two employees. The employee stationed at each window fills the order and takesthe money from customers arriving at the window. The average service time for this alternative is 3 minutes for each channel.1. What is the probability that no cars are in the system?2. What is the average number of cars waiting for service?3. What is the average number of cars in the system? What is the average time a car waits for service (in hours)?- Mom-and-Pop’s Grocery Store has a small adjacent parking lot with three parkingspaces reserved for the store’s customers. During store hours, cars enter the lot and useone of the spaces at a mean rate of 2 per hour. For n = 0, 1, 2, 3, the probability Pn that exactly n spaces currently are being used is P0 = 0.1, P1 = 0.2, P2 = 0.4, P3 = 0.3. - Midtown Bank always has two tellers on duty. The Customers arrive at checkouts at an average rate of 40 per hour. A cashier requires an average of 2 minutes to serve a customer. When both cashiers are busy, arriving customer joins a queue and wait to be served. From experience it is known that customers They wait in line for an average of 1 minute before going to the checkout. a) Describe why this is a waiting line system Mention the queuing model that can be implemented for the analysis (notation of Kendall) and why that model was chosenA fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. Consider a two-channel operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from customers arriving at the window.The average service time for this alternative is 2 minutes for each channel. What is the average time a car waits for service?
- A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. Consider a two-channel operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from customers arriving at the window. The average service time for this alternative is 3 minutes for each channel. What is the probability that no cars are in the system? What is the average number of cars waiting for service? What is the average number of cars in the system? What is the average time a car waits for service?BBA Bank (a fictitious one) has a drive-through teller window and observed that 15 customers arrive for service per hour, on an average, and the average service time per customer is 3 minutes. Assume inter-arrival time and service time follow a negative Exponential distribution. The bank hires you as a consultant. You guess that this is an M|M|1 system and you are required to determine the following: Probability (teller is busy) Probability (teller is idle) Probability of 3 customers in the system. Average number of customers waiting for service, that is, number of autos in the line excluding the one at the teller window. Average number of customers in the system, that is, number of autos in the line including the one at the teller window. Average time a customer spends in the system, that is, waiting time plus service time. Average time a customer spends in the waiting line before reaching the teller window.Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random. Assume that Poisson probability distribution with an arrival rate of 24 customers per hour or 0.4 customer per minute can be used to describe the arrival pattern. Assume further that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customer per minute. a. Use the single-channel drive-up bank teller operation to determine the probability that no customers are in the system b. Use the single-channel drive-up bank teller operation to determine the average number of customers waiting c. Use the single-channel drive-up bank teller operation to determine the average number of customers in the system