6Willow 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 48 customers per hour or 0.8 customers per minute.(a) What is the mean or expected number of customers that will arrive in a five-minute period?(b) 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 3customers will arrive during a five-minute period. (Round your answers to four decimal places.)X0123P(x)(c) Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur? (Round your answer to four decimal places.)

(a) 4(b)xP(x)00.018310.073320.146530.1954(c) 0.5665 Explanation:Approach to solving the question:The…

Answered: 6 Willow Brook National Bank operates a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 20 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 25 customers per hour. The manager’s service goal is to limit the waiting time prior to beginning the checkout process to no more than five minutes. Also the manager of Pete's Market wants to consider one of the following alternatives for improving service. Calculate the value of Wq for each alternative. Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 33 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations.Wq = 2.797 minutes Hire a second person to…
About 5% of hourly paid workers in a region earn the prevailing minimum wage or less. A grocery chain offers discount rates to companies that have at least 30 employees who earn the prevailing minimum wage or less. Complete parts (a) through (c) below. (a) Company A has 285 employees. What is the probability that Company A will get the discount? (Round to four decimal places as needed.) (b) Company B has 503 employees. What is the probability that Company B will get the discount? (Round to four decimal places as needed.) (c) Company C has 1002 employees. What is the probability that Company C will get the discount? (Round to four decimal places as needed.) (1,1) More Enter your answer in each of the answer boxes.
An aluminum foil manufacturer wants to improve the quality of his product and is trying to develop a probability model for the flaws that occur in a sheet of foil. Assume that X, the number of haws per square foot, has a Poisson distribution. If faws occur randomly at an average of one flaw per 90 square feet, what is the probability that a box containing a 270 square foot roll will contain more than one flaw? Round your answer to four decimal places, if necessary.
Airline passengers arrive at the passenger-screening facility of a major airport at the average rate of 12 passengers per minute. Suppose arrivals follow a Poisson distribution. What is the probability that 32 passenger arrives in a 3 minute interval? (Round answers to three decimal places.)
A single librarian is stationed at a reference desk of a university library that receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 11 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of 15 requests per hour. (Round your answers to four decimal places.) (a) What is the probability that no requests for assistance are in the system?
Show your complete solution.
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 48 customers per hour or 0.8 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 five-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 five-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 five-minute period. What is the probability that delays will occur? (Round your answer to four decimal places.)
A barbershop is operated by one barber and has a space capacity to accommodate for a total of 6 customers (including the one in service). If a customer comes to this shop and finds it full, he goes to other shops. Customers arrive according to Poisson distribution at a rate of 4.1 customers per hour. The barber’s service time is exponential and he can serve at a rate of 7.1 customers per hour. a. What is the probability that the barber is free? Answer = Answer b. What is the expected number of people in the system? Answer = Answer c. What is the expected waiting time in the queue? Answer = Answerhours. (hint: use effective arrival rate)
The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 13 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of 16 requests per hour. (Round your answers to four decimal places.) (a) What is the probability that no requests for assistance are in the system? (b) What is the average number of requests that will be waiting for service? (c) What is the average waiting time (in hours) before service begins? h (d) What is the average time (in hours) at the reference desk (waiting time plus service time)? h (e) What is the probability that a new arrival has to wait for service?
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. Let's assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 45 customers per hour, or 0.75 customers per minute. Determine the following operating characteristics for the system. (Round your answers to four decimal places.) (a) The probability that no customers are in the system 1353 (b) The average number of customers waiting 1786 (c) The average number of customers in the system 1.25 (d) The average time (in min) a customer spends waiting 4.2 X min (e) The average time (in min) a customer spends in the system x min 1 (f) The probability that arriving customers will have to wait for service 73 X
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 48 customers per hour or 0.8 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 five-minute period?
Cynthia's Mail Order Company provides free examination of its products for 7 days. If not completely satisfied, a customer can return the product within that period and get a full re- fund. According to past records of the company, an average of 2 of every 10 products sold by this company are returned for a refund. Using the Poisson probability distribution formula, find the probability that exactly 6 of the 40 products sold by this company on a given day will be returned for a refund.

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