The local one-person barber shop can accommodate a maximum of 5 people at atime (4 waiting and 1 getting hair-cut). Customers arrive according to a Poissondistribution with mean 5 per hour. The barber cuts hair at an average rate of 4per hour (Exponential service time).(a) What percentage of time is the barber idle?(b) What fraction of the potential customers are turned away?

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Answered: The local one-person barber shop can…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

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a sample of 4 students was taken and information about daily pocket money in tl (Y) and spending in tl (x) was collected
At any age, about 20% of American adults participate in fitness activities at least twice a week. However, these activities change as people get older, and occasionally participants cease to be older as they age. In a local survey of n = 100 adults over 40, a total of 15 people indicated that they participated in these activities at least twice a week. Does this data indicate that the percentage of participation for adults over 40 years of age is considerably less than the 20% figure? Find the p-value and use it to draw the appropriate conclusions.
The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 1000 cfs (cubic feet per second). a)Of the three randomly selected afternoons, what is the probability that on at least two afternoons the demand will exceed 700 cfs?
Ali Baba's Car Wash Service Centre is open 6 days a week, but its busiest day is always on Sunday. From the previous data, Ali Baba estimates that dirty cars arrive at the rate of one every two minutes, One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the following: iii) Compute the average time that a car spends in the system.
Do Left-Handers Die Earlier? According to a study published in the Journal of the American Public Health Association, lefthanded people do not die at an earlier age than right-handed people, contrary to the conclusion of a highly publicized report done 2 years earlier. The investigation involved a 6-year study of 3800 people in East Boston older than age 65. Researchers at Harvard University and the National Institute of Aging found that the “lefties” and “righties” died at exactly the same rate. “There was no difference, period,” said Dr. J. Guralnik, an epidemiologist at the institute and one of the coauthors of the report.
The Baytown Post Office has four stations for service. Cus-tomers line up in single file for service on an FIFO basis. The mean arrival rate is 40 per hour, Poisson distributed, and themean service time per server is five minutes, exponentially distributed. Compute the operating characteristics for this op-eration. Does the operation appear to be satisfactory in terms of: (a) postal workers’ (servers’) idle time; (b) customer wait-ing time and/or the number waiting for service; and (c) the percentage of the time a customer can walk in and get servedwithout waiting at all?
While trying to convince her friends that more than half of all sophomores live off-campus, Bren took a survey of a random sample of 129 sophomores and collected that among them 66 lived off-campus. Does this evidence support Bren's claim that more than half of all sophomores live off-campus at the 0.1 level of significance? p-value (round to four decimal places, use the cumulative table to find) = Conclusion (write R for "reject H0", and F for "fail to reject H0"):
The proportion p of residents in a community who recycle has traditionally been 70%. A policy maker claims that the proportion is less than 70% now that one of the recycling centers has been relocated. If 159 out of a random sample of 230 residents in the community said they recycle, is there enough evidence to support the policymaker's claim at the 0.10 level of significance?Perform a one-tailed test. Then complete the parts below.Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H0 and the alternative hypothesis H1. H0: H1: (b) Determine the type of test statistic to use. ▼(Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Is there enough evidence to support the policy maker's claim that the proportion of residents who…

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