Suggest a suitable distribution to model the number of customers arriving at the counter, X, per minute. b) State clearly any assumptions you have made by suggesting this model. c) Using your model, I. Find the probability that no customer arrive in a given minute. II. Find the probability that at most 4 customers arrive in a given minute. III. In any given 4 minutes period, find ? such that ?(? > ?) = 0.0487. IV. Check the answer of part I
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Customers arrive at a bank counter at an average rate of 3
customers per hour.
a) Suggest a suitable distribution to model the number of
customers arriving at the counter, X, per minute.
b) State clearly any assumptions you have made by suggesting
this model.
c) Using your model,
I. Find the probability that no customer arrive in a given
minute.
II. Find the probability that at most 4 customers arrive in a
given 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.
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Solved in 2 steps with 1 images
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How does FedEx’s money-back guarantee address customers’ concerns about heterogeneity?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.)Provide instead: 3 Positive and 3 negative outcomes for forecasting 3 Positive and 3 negative outcomes for queuing model
- Suppose the waiting time at a certain checkout counter is bi-modal. With probability 0.85, the waiting time follows an exponential distribution with a mean waiting time of four minutes. With probability 0.15, the waiting time equals 20 minutes. a) Compute the mean and median waiting time at the checkout counter. b) Compute the variance of the waiting time at the checkout counter. c) Compute the probability that an individual customer waits longer than 5 minutes at the checkout counter.A. Know some of the basic queue performance measure B. Identify the relationships between queues and some statistical distributionAssume that during minute t (the current minute isminute 1), the following sequence of events occurs: (1) Atthe beginning of the minute, xt customers arrive at the cashregister; (2) the store manager decides how many cashregisters should be operated during the current minute;(3) if s cash registers are operated and i customers arepresent (including the current minute’s arrivals), c(s, i)customers complete service; and (4) the next minute begins.A cost of 10¢ is assessed for each minute a customerspends waiting to check out (this time includes checkouttime). Assume that it costs c(s) cents to operate s cashregisters for 1 minute. Formulate a dynamic programmingrecursion that minimizes the sum of holding and servicecosts during the next 60 minutes. Assume that before thefirst minute’s arrivals, no customers are present and thatholding cost is assessed at the end of each minute.
- Please do not give solution in image format thanku 1. In a queueing system, customers arrive once every 4 seconds (standard deviation = 4) and services take 3 seconds (standard deviation = 5.1). What is the average time a customer wiill spend in the system (in seconds)?The likely be used to describe the distribution of time between arrivals of customers at the grocery store. Multiple Choice O O distribution would most O O normal uniform binomial exponentialNeve Commercial Bank is the only bank in the town of York, Pennsylvania. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is currently one teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times may be described by the negative exponential distribution. If asingle teller is used, find:a) The average number in the system.b) The probability that the bank is empty.c)CEO Benjamin Neve is considering adding a second teller (who would work at the same rate as the first) to reduce the waiting time for customers. A single line would be used, and the customer at the front of the line would go to the first available bank teller. He assumes that this will cut the waiting time in half. If a second teller is added, find the new answers to parts (a) to (e).
- 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…Suggest 3- 4 ways to reduce queue waiting times in restaurant during covid 19In Queuing Theory, statistical pattern by which customers arrive over a period of time, follows 1. Binomial distribution 2. Normal distribution 3. Poisson distribution 4. Long-normal distribution