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 traffic accidents at a certain intersection is thought to be well modeled by a Poisson process with a mean of 3 accidents per year. Find the probability that less than three months elapse between accidents.
Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random. Assume that Poisson probability distribution with an arrival rate of 24 customers per hour or 0.4 customer per minute can be used to describe the arrival pattern. Assume further that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customer per minute a.Use the single-channel drive-up bank teller operation to determine the average arrival time in minutes of customers b.Use the single-channel drive-up bank teller operation to determine the average service time in minutes of the drive-up teller.
In a specific area, this period of time, it is believed that the number of thunderbolts that are falling is distributed according to the Poisson distribution with a rate of 75 thunderbolts per hour. In the next questions give your answer as a decimal number correct in three decimal places. During a specific minute time, find the probability that: (i) there are no thunderbolts in the area.(ii) at least one thunderbolt hits the area.
How many even three-digit numbers can be formed from the digits 1,2,3,5,6,8 and 9 if each digit can be used only once?
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.)
Yhmeer is watching a shower of meteors (shooting stars). During the shower, he sees meteors at an average rate of 1.3 per minute. (a) State the conditions required for a Poisson distribution to be a suitable model for the number of meteors which Yhmeer sees during a randomly selected minute (b) Using Excel or otherwise, determine the probability that, during one minute, Yhmeer sees (i) exactly one meteor (ii) at least 4 meteors
Hits to a high-volume website are assumed to follow a Poisson distribution with a mean of 1200 per day. What is the probability that the number of hits to the website tomorrow will be between 1190 and 1220 (inclusive)?
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.
(a) On the average, it is known that 6 customers arrive at a restaurant per hour according to a Poisson distribution. Find the probability that 10 customers arrived at the restaurant in the next hour. (i) (ii) (iii) 5 to 7 customers arrived at the restaurant in the next 2 hours. less than I customer arrived at the restaurant in the next 30 minutes. (b) Suppose the probability that there will be no cars arriving at a service centre per hour is 0.20. Determine the expected number of cars that will arrive at the service centre in the next hour.
(c) Does this Poisson distribution provide a good model for the number of accidents in this example (as per Table 1)? Explain why or why not. Use R to produce a graph to help support your answer (produce the R as part of your answer). (d) Use the model in (b) to estimate the probability that less than 2 accidents were recorded in any randomly chosen week. How does this compare to the actual data?
A company advertise their products on Instagram. The number of times their advertise- ments are clicked on follows a Poisson distribution with a rate of 18 clicks per minute.

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