**Poisson Process for Structural Loads**An article suggests that a Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is 0.4 year.- **(a)** How many loads can be expected to occur during a 4-year period? - *Answer: [_____] loads*- **(b)** What is the probability that more than eleven loads occur during a 4-year period? (Round your answer to three decimal places.) - *Answer: [_____]*- **(c)** How long must a time period be so that the probability of no loads occurring during that period is at most 0.2? (Round your answer to four decimal places.) - *Answer: [_____] yr*

Answered: Image /qna-images/answer/27a5c47b-dd6a-495e-bcfb-7e57a82b21cd.jpg

Answered: An article suggests that a Poisson…

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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Crime reports from 2019 indicate that 6.2 motor vehicle thefts occur each hour in the United States. Assume that the distribution of thefts per hour can be approximated by the Poisson probability distribution. Calculate the probability that exactly 4 thefts occur in an hour.
The waiting time T at a bank teller’s window between two successive customers isdistributed as exponential with a mean of four minutes. Find the following probabilities:(a) P(T ≥ 5, (b) P(3 ≤ T ≤ 6), (c) P(T ≤ 4), and (d) P(T < 5). NOTE: Please explain each part, so the problem can be used as a Study Guide
The useful life of Johnson rods for use in a particular vehicle follows an exponential distribution with an average useful life of 5.2 years.You have a three-year warranty on your vehicle’s Johnson rod. What is the probability that the Johnson rod doesn’t fail before then? That is, what is the probability that its useful life doesn’t end before three years?b.If the vehicle manufacturer wants to limit the number of claims on the three-year warranty to 20%, what should the average useful life of the Johnson rod be?
If arrivals occur at a mean rate of 2.6 events per minute the exponential probability of waiting more than 1.5 minutes for the next arrival is is a .0202 or .0122 or .0535 or .2564
Discuss the connection between the Poisson and exponential distributions.
The time between failures of our video streaming service follows an exponential distribution with a mean of 40 days. Our servers have been running for 17 days, What is the probability that they will run for at least 97 days? (clarification: run for at least another 80 days given that they have been running 17 days). Report your answer to 3 decimal places.
An IPHONE has an advertised failure rate of 0.01 per hour. The failure rate is constant and the exponential distribution applies. (a) What is the mean time to failure? (b) What is the probability that 300 hours will pass before a failure is observed? (a) The mean time to failure is hours. (Type an integer or a decimal. Do not round.) (b) The probability that 300 hours will pass before a failure is observed is (Round to four decimal places as needed.)
A university is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 18 per hour. It takes an average of 2 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed. What is the arrival rate? (Include the units.) What is the service rate? (Include the units.) Find the probability that the employee is idle.
Data collected at an airport suggests that an exponential distribution with mean value 2.435 hours is a good model for rainfall duration. (a) What is the probability that the duration of a particular rainfall event at this location is at least 2 hours? At most 3 hours? Between 2 and 3 hours? (Round your answers to four decimal places.) at least 2 hours at most 3 hours between 2 and 3 hours (b) What is the probability that rainfall duration exceeds the mean value by more than 3 standard deviations? (Round your answer to four decimal places.) What is the probability that it is less than the mean value by more than one standard deviation?
Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…
Please solve (b) only!

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