lec 3: Poisson Probability Distribution |Problems: 5.71, 5.72, 5.73

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In this lecture, we will solve Poisson distribution exercise problems from Chapter 5 of Probability & Statistics for Engineers and Scientists by Walpole, providing clear explanations and step-by-step solutions. Whether you're a student or just a statistics enthusiast, this video will help you understand these concepts. We will also solve 3 problems here
5.71 For a certain type of copper wire, it is known that, on the average, 1.5 flaws occur per millimeter. Assuming that the number of flaws is a Poisson random variable, what is the probability that no flaws occur in a certain portion of wire of length 5 millimeters? What is the mean number of flaws in a portion of length 5 millimeters?
5.72 Potholes on a highway can be a serious problem, and are in constant need of repair. With a particular type of terrain and make of concrete, past experience suggests that there are, on the average, 2 potholes per mile after a certain amount of usage. It is assumed that the Poisson process applies to the random variable “number of potholes.”
(a) What is the probability that no more than one pothole will appear in a section of 1 mile?
(b) What is the probability that no more than 4 potholes will occur in a given section of 5 miles?
5.73 Hospital administrators in large cities anguish about traffic in emergency rooms. At a particular hospital in a large city, the staff on hand cannot accommodate the patient traffic if there are more than 10 emergency cases in a given hour. It is assumed that patient arrival follows a Poisson process, and historical data suggest that, on the average, 5 emergencies arrive per hour.
What is the probability that in a given hour the staff cannot accommodate the patient traffic.
What is the probability that more than 20 emergencies arrive during a 3-hour shift?
Course: Probability & Statistics
Topic: Poisson Probability Distribution |Problems: 5.71, 5.72, 5.73
Probability & Statistics for Engineers and Scientists, by Walpole chapter: 5
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