Auto vehicles arrive at a petrol pump with one petrol unit in Poisson fashion, averaging 10 units per hour. The service time is distributed exponentially with a mean of 3 minutes. Find the following:a)    Average number of units in the systemb)    Average waiting time for customersc)    The average length of the queued)    The probability that a customer arriving at the pump will have to wait.e)    The utilization factor for the petrol pumpf)    The probability that the number of customers in the system is 2.

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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Auto vehicles arrive at a petrol pump with one petrol unit in Poisson fashion, averaging 10 units per hour. The service time is distributed exponentially with a mean of 3 minutes. Find the following:
a)    Average number of units in the system
b)    Average waiting time for customers
c)    The average length of the queue
d)    The probability that a customer arriving at the pump will have to wait.
e)    The utilization factor for the petrol pump
f)    The probability that the number of customers in the system is 2. 

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