The number of tickets issued by a meter reader for parking- meter violations can be modeled by a Poisson distribution with a rate parameter of six tickets per hour. What is the probability that at least three tickets are given out during a particular hour? How many tickets do you expect to be given during a 20-min period?
The number of tickets issued by a meter reader for parking- meter violations can be modeled by a Poisson distribution with a rate parameter of six tickets per hour. What is the probability that at least three tickets are given out during a particular hour? How many tickets do you expect to be given during a 20-min period?
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:**Poisson Distribution in Parking Meter Violations**
The number of tickets issued by a meter reader for parking-meter violations can be modeled by a Poisson distribution with a rate parameter of six tickets per hour.
**Problem 1: Probability Calculation**
- **Question:** What is the probability that at least three tickets are given out during a particular hour?
- **Solution Box:** (Insert your solution here)
**Problem 2: Expected Tickets Calculation**
- **Question:** How many tickets do you expect to be given during a 20-minute period?
- **Solution Box:** (Insert your solution here)
In the Poisson distribution context, the key element is the "rate parameter" which tells us the average number of occurrences (tickets in this case) in a fixed interval (one hour).
- For problem 1, you would calculate the cumulative probability of fewer than three tickets and subtract from 1.
- For problem 2, convert the hourly rate to a 20-minute period by adjusting the rate parameter accordingly.
Understanding these problems helps in learning the application of Poisson distribution in real-world scenarios.
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