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- 44. US Airlines receives an average of 500 calls per hourfrom customers who want to make reservations, wherethe times between calls follow an exponential distribution. It takes an average of three minutes to handleeach call. Each customer who buys a ticket contributes$100 to US Airlines profit. It costs $15 per hour tostaff a telephone line. Any customer who receives abusy signal will purchase a ticket from another airline. How many telephone lines should US Airlineshave? Base your answer on an appropriate simulation.Does it matter whether the service times are exponentially distributed or gamma distributed? Experimentto find out.Based on Kolesar et al. (1974), Metropolis PD Precinct 88 must determine the minimum number of police cars required to meet its needs for the next 24 hours. An average call for service requires 30minutes. The number of calls the police department expects to receive during each hour is shown in the file P12_61.xlsx. The Metropolis PD standard of service is that there should be a 90% chance that a car is avail-able to respond to a call. For each of the following,discuss how you might find a solution.a. Suppose that patrol officer teams assigned to a car work an 8-hour shift beginning at 12 a.m., 8 a.m., or 4 p.m. Officers get an hour off for a meal. This hour can be anytime between the second and fifthhour of their shift. The precinct wants to know how many teams are needed to meet daily demand.b. Suppose that patrol officer teams assigned to a car begin their 8-hour shifts at 12 a.m., 8 a.m., 12 p.m., 4 p.m., and 8 p.m. An hour off for meals may be taken anytime during a shift. The…Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2.5per minute. The average time to handle each is 10seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation. a) The probability that the operator is busy = enter your response here (round your response to two decimal places). b) The average time that a caller must wait before reaching the operator = enter your response here minutes (round your response to two decimal places). c) The average number of calls waiting to be answered = enter your response here calls (round your response to two decimal places).
- The average time between the arrivals of the taxis arriving at the airport to pick up passengers has an exponential distribution, with an average of 10 minutes. a) What is the probability that a passenger will wait for the taxi less than 15 minutes? b) What is the probability that a passenger will wait for the taxi between 20 and 30 minutes? Solve using the cumulative distribution function H1Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2.0 per minute. The average time to handle each is 15 seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation. The probability that the operator is busy = 0.500.50 (round your response to two decimal places).The average time that a caller must wait before reaching the operator = 0.250.25 minutes (round your response to two decimal places). c) The average number of calls waiting to be answered = calls (round your response to two decimal places).. For the MyMy1 queueing model, why do the following results hold? (Hint: Remember that 1ym is the meanservice time. Then think how long a typical arrival must wait in the system or in the queue.) a. W 5 (L 1 1)ym b. WQ 5 Lym
- Use the RAND function and the Copy command to generate 100 random numbers. a. What fraction of the random numbers are smaller than 0.5? b. What fraction of the time is a random number less than 0.5 followed by a random number greater than 0.5? c. What fraction of the random numbers are larger than 0.8? d. Freeze these random numbers. However, instead of pasting them over the original random numbers, paste them onto a new range. Then press the F9 recalculate key. The original random numbers should change, but the pasted copy should remain the same.US Airlines receives an average of 500 calls per hour from customers who want to make reservations, where the times between calls follow an exponential distribution. It takes an average of three minutes to handle each call. Each customer who buys a ticket contributes $100 to US Airlines profit. It costs $15 per hour to staff a telephone line. Any customer who receives a busy signal will purchase a ticket from another airline. How many telephone lines should US Airlines have? Base your answer on an appropriate simulation. Does it matter whether the service times are exponentially distributed or gamma distributed? Experiment to find out.Consider the interval of random numbers presented below. The following random numbers have been generated: 99, 98, 26, 09, 49, 52, 33, 89, 21, 37. Simulate 10 hours of arrivals at this gas station. What is the average number of arrivals during this period?
- In the PMT function, what is not true about the Num_periods argument? Group of answer choices It reflects a count of how many times payments will be made. It can contain references to fields. You must use constants for this argument. It is required.Dr. Tarun Gupta, a Michigan vet, is running a rabies vaccination clinic for dogs at the local grade school. Tarun can "shoot" a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of one dog every 6 minutes according to a Poisson distribution. Also assume that Tarun's shooting times are negative exponentially distributed. a) The probability that Tarun is idle = enter your response here (round your response to two decimal places). b) The proportion of the time that Tarun is busy = enter your response here (round your response to two decimal places). c) The average number of dogs being vaccinated and waiting to be vaccinated = enter your response here dogs (round your response to two decimal places).Bad simulations Explain why each of the followingsimulations fails to model the real situation properly:a) Use a random integer from 0 through 9 to representthe number of heads when 9 coins are tossed. b) A basketball player takes a foul shot. Look at a ran-dom digit, using an odd digit to represent a good shot and an even digit to represent a miss.c) Use random numbers from 1 through 13 to represent thedenominations of the cards in a five-card poker hand.