Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 5.5 per year. Find the probability that, in a year, there will be 4 hurricanes. In a 55-year period, how many years are expected to have 4 hurricanes? How does the result from part (b) compare to a recent period of 55 years in which 8 years had 4 hurricanes? Does the Poisson distribution work well here?

Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 5.5 per year. Find the probability that, in a year, there will be 4 hurricanes. In a 55-year period, how many years are expected to have 4 hurricanes? How does the result from part (b) compare to a recent period of 55 years in which 8 years had 4 hurricanes? Does the Poisson distribution work well here?

Name: Assume that the Poisson distribution applies and that the mean number
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 5.5 per year.Find the probability that, in a year, there will be 4 hurricanes.In a 55-year period, how many years are expected to have 4 hurri

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 27T

See similar textbooks

Similar questions

Suppose the number of babies born during an 8-hour shift at a hospital's maternity wing follows a Poisson distribution with a mean of 6 an hour. Find the probability that five babies are born during a particular 1-hour period in this maternity wing.
A call center agent receives an average of 28 calls per hour. Assuming that this follows a Poisson distribution, use the normal approximation to determine the probability that in an hour, the call center agent will receive: 32 or more calls. greater than 25 calls. exactly 44 calls.
For the 55-year period since 1960, there were 336 Atlantic hurricanes. Assuming the Poisson distribution, a) find µ, the mean number of hurricanes per year; b) find the probability that in a randomly selected year, there are exactly 8 hurricanes; c) in this 55-year period, there were actually 5 years with 8 Atlantic hurricanes. How does this actual result compare to the probability found in part (b)? Does the Poisson distribution appear to be a good model in this case?
A manufacturing company claims that the number of machine breakdowns follows a Poisson distribution with a mean of two breakdowns every 500 hours. Let x denote the time (in hours0 between successive breakdowns. assuming that the manufacturing company's claim is true, find the probability that the time between successive breakdowns is at most five hours.
The number of industrial injuries per working week in a particular factory is known to follow a Poisson distribution with mean 0.5. Find the probability that in a particular week there will be less than 2 accidents. Express your answer in 4 decimal place value
In the hour before noon, a busy corporation switchboard received an average of 55 calls. What is the probability that more than 70 calls will be received during this hour? What is the probability that fewer than 50 calls will be received during this hour? What is the probability that between 50 and 70 calls will be received during this hour? (Use the normal approx. to the Poisson distribution, without the continuity correction.
The number of errors per 1000 words made by a particular typist has a Poisson distribution with a mean of 2.5.(a) Find the probability that, in a 4000 word script, there should at least be 14 typing errors.(b) Using a suitable approximation, show that the probability will be more than 25 errors in a 10000 word dissertation.
The time between successive calls to a corporate office is exponentially distributed with a mean of 10 minutes. Assume that the times between successive calls are independent of each other. Thus, the calls arrive according to a Poisson process. What is the probability that there are more than two calls in a 20 minutes interval?
The number of traffic accidents at a certain intersection is thought to be well modelled by a Poisson process with a mean of 3.5 accidents per year. (a) Find the mean waiting time between accidents. (b) Find the probability that less than one month elapses between accidents. (c) If no accidents have occurred within the last six months, what is the probability that an accident will occur within the next year?