18It can be shown that if events are occurring in time according to a Poisson distribution with mean it, then the interarrival times between events have an1exponential distribution with mean If calls come into a police emergency center at the rate of eight per hour, what is the probability that more than217 minutes will elapse between the next two calls? (Round your answer to four decimal places.)

The calls come into a police emergency center at the rate of 8 per hour.The events occurring in time…

Answered: It can be shown that if events are…

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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Similar questions

A microprocessor that controls the tuner in color TVs fails completely at random (that is, according to the exponential distribution). Suppose that the likelihood that a microprocessor that has survived for k years fails in year k + 1 is .0036. What is the cumulative distribution function of the time until failure of the microprocessor?
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?
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.
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?
Suppose that the lifetime of a soft white light bulb follows an exponential distribution with expected value 300 hours, and the lifetime of an bright white light bulb follows an exponential distribution with expected value 700 hours, and the two lifetimes are independent. If we start using both light bulbs at the same time, then what is the probability that the soft white light bulb will burn out before the bright white light bulb?
The Poisson distribution gives the probability for the number of occurrences for a "rare" event. Now, let x be a random variable that represents the waiting time between rare events. Using some mathematics, it can be shown that x has an exponential distribution. Let x > 0 be a random variable and let β > 0 be a constant. Then y = 1 β e−x/β is a curve representing the exponential distribution. Areas under this curve give us exponential probabilities. If a and b are any numbers such that 0 < a < b, then using some extra mathematics, it can be shown that the area under the curve above the interval [a, b] is the following. P(a < x < b) = e−a/β − e−b/β Notice that by definition, x cannot be negative, so, P(x < 0) = 0. The random variable x is called an exponential random variable. Using some more mathematics, it can be shown that the mean and standard deviation of x are the following. μ = β and σ = β Note: The number e = 2.71828 is used throughout…
The annual rainfall (in inches) in a certain region is normally distributed with mean = 40 and o=4. What is the probability that starting with this year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? What assumption are you making?
indicate the units to the final answer if any Draw the necessary graph if any. Round off to four decimal places or in lowest term if your answer is in fraction.
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.…

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