Round off answers to two decimal points(1)Phone calls in a customer service center arrive accordingto a Poisson process with rate of 6 calls per minute. For eachcall, the probability that it is a complaint is given by aBernoulli distribution with parameter 0.3.Find(i) the expected number of complaints received in any givenone hour period(ii) the standard deviation of the number of complaintsreceived in one hour(iii) what is the probability that the center receives more than120 complaints in any given one hour period?

calls per minute (rate of calls) probability of a complaint

Answered: (1)Phone calls in a customer service…

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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The number of work-related injuries per month in a manufacturing plant is known to follow a Poisson distribution, with a mean of 4.0 work-related injuries a month. What is the probability that in a given month, no work-related injuries occur? That at least one work-related injury occurs?
Person P is walking with his dog every day. He decides to model the time intervals between dog encounters (i.e., how long does it take between two encounters) with the independent random variables Y₁, . . ., Yn . Number of dogs encounters per day, the number of customers entering a store per hour, the number of bacteria per liter of water, etc. are classically modelled using the Poisson distribution. With an exponential distribution, on the other hand, is used for modelling intervals of between events and how long a light bulb lasts, for example. After learning this, person P decides to model the observations in such a way that the corresponding random variables Y1,..., Yn for a random sample, that is, independent observation, of the exponential distribution Exp(1/µ), µ > 0. The parameter µ > 0 is used as the statistical model parameter 1 which is the expected value of each observation random variable Yi. (a) Form the maximum likelihood estimate μ^(y) in the model for the parameter μ…
The number of bankruptcies filed in the district court has a Poisson distribution with an average of 6 per week. (a) What is the probability that there will be no bankruptcy filings during a given week? (Round your answer to three decimal places.) (b) What is the probability that there will be at least one bankruptcy filing during a given week? (Round your answer to three decimal places.) (c) Within what limits does Tchebysheff's Theorem suggest you would expect to see the number of bankruptcy filings per week at least 88.88% of the time? (Round your answer up to the nearest whole number.)
An airport has 3 security lines, with each line capable of scanning 290 people per hour. People arrive in front of the security line at the rate of 850 per hour. Make the standard assumption of a Poisson distribution for arrivals and an exponential distribution for service times, and calculate the following: What is the probability that there are no people in the waiting line? Answer is NOT 0.02. What is the average length (number of people) in the waiting line? Answer is NOT 41.52.

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