Customers arrive at a carwash on average once every 40 minutes. It seems likely that customer arrivals follow an exponential distribution. For each of these random numbers, calculate the simulated time between arrivals at the carwash. (Round your answers the nearest whole number.) Random Number Time Between Arrivals 0.27 0.84 0.23
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- 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, with an arrival rate of 30 customers per hour or 0.5 customers per minute. Assume the Poisson probability distribution can be used to describe the arrival process. (a) What is the mean or expected number of customers that will arrive in a six-minute period? (b) Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a six-minute period. (Round your answers to four decimal places.) X 0 1 2 3 P(x) (c) Delays are expected if more than three customers arrive during any six-minute period. What is the probability that delays will occur? (Round your answer to four decimal places.)In a queueing system, customers arrive once every 5 minutes (standard deviation = 7) and services take 3 minutes (standard deviation = 6.8). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average time a customer will spend in the system (in minutes)? minutesIn a queueing system, customers arrive once every 4 minutes (standard deviation = 7) and services take 3 minutes (standard deviation = 5.5). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average time a customer will spend in the queue (in minutes)? minutes
- Granos, Inc. purchased new automated coffee vending machines, the Preso 2000. This Preso 2000 requires a constant 45 seconds to produce a coffee. It has been estimated that customers will arrive at the vending machine according to a Poisson distribution at an average of one every 50 seconds. To help determine the amount of space needed for the line in front of the vending machine, Granos, Inc. would like to know the expected average time in the system, the average line length (in costumers), and the average number of costumers in the system (both in line and at the vending machine).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, with an arrival rate of 24 customers per hour or 0.4 customers per minute. What is the mean or expected number of customers that will arrive in a five-minute period?λ = fill in the blank 1 per five minute period Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period. If required, round your answers to four decimal places. x P(x) 0 fill in the blank 2 1 fill in the blank 3 2 fill in the blank 4 3 fill in the blank 5 Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur? If required, round your…In a queueing system, customers arrive once every 6 seconds (standard deviation = 5) and services take 5 seconds (standard deviation = 4). (Do nót round intermediate calculations. Round your answer to three decimal places.) customers What is the average number of customers in the queue?
- Customers arrive at a bank counter at an average rate of 3customers per hour.a) Suggest a suitable distribution to model the number ofcustomers arriving at the counter, X, per minute.b) State clearly any assumptions you have made by suggestingthis model.c) Using your model,I. Find the probability that no customer arrive in a givenminute.II. Find the probability that at most 4 customers arrive in agiven minute.III. In any given 4 minutes period, find ? such that?(? > ?) = 0.0487.IV. Check the answer of part I and part ii using RStudio.In a queueing system, customers arrive once every 4 seconds (standard deviation = 4) and services take 2 seconds (standard deviation = 4.3). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average time a customer will spend in the queue (in seconds)? secondsIn a queueing system, customers arrive once every 4 hours (standard deviation = 7) and services take 3 hours (standard deviation = 4.9). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average number of customers in the queue? customers
- In a queueing system, customers arrive once every 4 seconds (standard deviation = 4) and services take 2 seconds (standard deviation = 4.3). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average number of customers in the queue? customersWould you expect the Poisson distribution to be a good approximation of a) Runners crossing the finish line in the Boston Marathon? b) Arrival times of the students in your OSCM class?The manager of a call center recorded the volume of calls received between 9 and 10 a.m. for 21 days and wants to obtain a seasonal index for each day for that hour. Day Volume Day Volume Day Volume Tues 67 Tues 60 Tues 64 Wed 75 Wed 73 Wed 76 Thurs 82 Thurs 85 Thurs 87Fri 98 Fri 99 Fri 96 Sat 90 Sat 86 Sat 88 Sun 36 Sun 40 Sun 44 Mon 55 Mon 52 Mon 50?