Customers arrive at a suburban ticket outlet at the rate of14 per hour on Monday mornings. This can be describedby a Poisson distribution. Selling the tickets and providinggeneral information takes an average of 3 minutes percustomer, and varies exponentially. Determine averagetime in line and average time in the system.Select one:O a. Average time in line 4 minutes and average timein the system 7 minutesO b. Average time in line 7 minutes and average timein the system 10 minutesO c. Average time in line 2 minutes and average timein the system 5 minutesO d. Average time in line 3 minutes and average timein the system 6 minutes

Given that Arrival rate =14 hour per hour Service rate =3 minutes Then we have to find determine…

Answered: Customers arrive at a suburban ticket…

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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Tracy and Diane, working as twohairstylists at coiffeur, dress hair of women at a rate of 3 women per hour. The hairdressing time for Tracy and Dianeis exponentially distributed. Women arrive to the coiffeur according to a Poisson distribution with a rate of 5 per hour.a) What is the probability that Tracy is busy? b) What is the probability that Diane is idle? c)On average, how many women are waiting for hairdressing? d)On average, how long must a woman wait before hairdressing begins? e) What is the average time a woman spends in the coiffeur? f) Find the probability that a woman’s waiting time in the coiffeur is more than 90 minutes?
An airline is planning to open a satellite desk in a new area. Requests for tickets and information will average 4.5 minutes arrival rate in the form of Poisson distribution whereas service time is 2.8 minutes. Determine service time Select one: a.20.18 b.22.56 c. 21.43 d.19.34 e.21.45
In a certain garden which has been treated with agro chemicals, new plants grow at an average rate of 10% within a square meter. When this same garden is not treated with agro chemicals, plants grow at an average rate of 30% within a square meter. You may assume that the number of plants that grow in the garden may be modelled by a Poisson distribution. Mr Amankwah Amaniapong has a rectangular garden measuring seven-hundred centimeters by three hundred centimeters. He uses these same agro chemicals to treat his garden. Mrs. Amankwah Amaniapong also has a rectangular garden with a dimension of five hundred centimeters by four hundred centimeters. She has decided not to apply these agro-chemicals in her garden. Find the probability that: 1. Mr. Amankwah Amaniapong’s garden has exactly 4 plants;2. Mrs. Amankwah Amaniapong’s garden has at least 6 but fewer than 10 plants;3. Mr. Amankwah Amaniapong has at least one plant and Mrs. Amankwah Amaniapong’s garden has none.
A burger joint has on average 9 customers arriving per hour. There is only one employee serving customers and she takes about 4 minutes on average to serve a customer. The burger joint is open 10 hours per day and makes a profit of $10 for each burger sold. The staff has a pay rate of $20/hour. Assume a Poisson distribution on the arrival rate of customers and exponential distribution on the service time of the employee. Q. If customers do not want to spend more than 6 minutes in the burger joint (including waiting and service), how much potential profit would the joint lose per day?
(a) Auto vehicles arrive at a petrol pump, having one petrol unit, in Poisson fashion with anaverage of 10 units per hour. The service time is distributed exponentially with a mean of3 minutes. Find the following:i. Average number of units in the system ii. Average waiting time iii. Average length of queue

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