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Vehicles arriving at random at a one-lane toll booth at an average rate of five vehicles/minute. What is the probability of not observing any vehicle over a 30-second period? What is the probability of collecting tolls from exactly six vehicles in one minute?

Vehicles arriving at random at a one-lane toll booth at an average rate of five vehicles/minute. What is the probability of not observing any vehicle over a 30-second period? What is the probability of collecting tolls from exactly six vehicles in one minute?

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Vehicles arriving at random at a one-lane toll booth at an average rate of five vehicles/minute. What is the probability of not observing any vehicle over a 30-second period? What is the probability of collecting tolls from exactly six vehicles in one minute?
Transcribed Image Text:Vehicles arriving at random at a one-lane toll booth at an average rate of five vehicles/minute. What is the probability of not observing any vehicle over a 30-second period? What is the probability of collecting tolls from exactly six vehicles in one minute?
Expert Solution
Step 1

Given:-

Average rate of vehicles = 5 vehicles/minute

To find:-

Probability of not observing any vehicle over 30 second period

Probability of collecting tolls from exactly six vehicles in one minute

Concept:-

The formula for the Poisson's distribution is given by

Px=e-λ×λxx!Wheree=Base of logarithmx=Random valueλ=Average rate of value

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