Suppose that visitors to a state carnival which is open from 5 pm to 10 pm daily arrive according toa non-homogeneous Poisson process. The rate at which visitors arrive decreases linearly from 30 perhour at 5 pm to 5 per hour at 10 pm. How many visitors are expected to arrive between 7 pm and 9pm?

For a non-homogenous Poisson process with rate λt, the number of arrivals in any interval is a…

Answered: Suppose that visitors to a state…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
A bank has established two counters, one for commercial banking and the second for personal banking. Arrival and service rates at the commercial counter are 6 and 12, respectively. The corresponding numbers at the personal banking counter are respectively 12 and 24. Assume that arrivals occur in Poisson processes and service times are exponentially distributed. (5.2) What is the effect of operating the two queues as a two server queue with arrival rate 18 per hour. What conclusion can you draw from this operation?
A car servicing station has 2 bays where service can be offered simultaneously. Because of space limitation, only 4 cars are accepted for servicing. The arrival pattern is Poisson with 12 cars per day. The service time in both the bays is exponentially distributed with µ = 8 cars per day per bay. Find the average number of cars in the service station, the average number of cars waiting for service and the average time a car spends in the system.
Suppose that the incidence rate pf myocardial infraction (MI) was 5 per 100 among 45 - 50 year old men in 2000. To look at changes in incidence over time, 5000 men in this age groups were followed for 1 year starting in 2010. Twenty new cases of MI were found. Suppose we eventually plan to accumulate 50 MI cases during the period 2010-2015. Suppose that 20% of the patients with MI in 2000 died within 24 hours. This proportion is called the 24 hour case fatality rate. A test is performed to see if the true proportion of 24 hour case fatality rate differs from 20%, with significance level of 0.01. Assume that the 24-hour case fatality rate is truly 25% during the period. how large a sample is needed to achieve 92% power?
Moore’s portable X-ray equipment repair service shop receives an average of 6 portable X-ray sets per 8-hour day to be repaired. Moore would like to be able to tell his customers that they can expect one day service. What average repair time per set will the repair shop have to achieve to provide 1-day service on average? Assume that the arrival rate is Poisson distributed and repair times are exponentially distributed.
Please answer the 3 questions
Suppose that the number of customers arriving to a store follows the Poisson process with rate 1/λ per minute. Choose an option that is not correct. The expected number of customers arriving to the store between 9am and 11am is twice bigger than the expected number of customers arriving to the store between 10am and 11am. The number of customers arriving to the store between 9am and 10am is independent of the number of customers arriving to the store between 10am and 11am. The expected number of customers arriving to the store between 9am and 10am is 60λ. The number of customers arriving to the store between 9am and 10am follows the same distribution as the number of customers arriving to the store between 10am and 11am
Suppose that the login times to a computer network follows a Poisson process with an average of 4 logins per minute. Find the probability of exactly 6 logins in 2 minutes.
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The service charge for repairs at an automobile service center is based on a standard time specified for each type of repair. The time specified for the replacement of the universal joint a driveshaft is one hour. To better serve the customers, the management would like to change the time specified in their service fee rates. The manager reviews such repairs and assumed that the workers are working faster than the standard time. The manager observed 30 of such repairs and gets an average repair time of 0.86 hours with a standard deviation of 0.32 hours. Test at the 1% level of significance the null hypothesis for the actual average time for this repair. Show the following steps. a. Formulation of the hypothesis and identifying the claimb. Determining what test to be usedc. Identifying the significance level and critical valued. Computation of the test statistice. Comparing the absolute value of the computed test statictic and critical value, decide whether null hypothesis is accepter…
4. A machine works for an exponentially distributed time with rate u and then fails. A repair crew checks the machine at times distributed according to a Poisson process with rate A; if the machine is found to have failed then it is immediately replaced. Find the expected time between replacements of machines.
Laureysens, et al. (2004) studied the concentration of aluminum in wood from a number of clones of poplar growing in an area with heavy pollution. The same clone was sampled and tested once in August and again in November. The researchers believed that the concentration of aluminum would be shown to be increasing over time and hence higher in November than in August. The following table gives the aluminum concentrations for twelve of the clones. Clone 1 2 3 4 5 6 7 8 9 10 11 12 Aug. 8.1 10.0 16.5 13.6 9.5 8.3 18.3 13.3 7.9 8.1 8.9 13.4 Nov. 11.2 16.3 15.3 15.6 10.5 15.5 12.7 11.1 19.9 20.4 14.2 36.8 Diff. 3.1 6.3 1.2 2.0 1.0 7.2 5.6 2.2 12.0 12.3 5.3 23.4 The data are to be analyzed using the Wilcoxon signed rank test. H0: Values of aluminum concentrations in the 2 months have the same distribution. Ha: Values of aluminum concentrations are systematically larger in November than in August. Fix α = 0.05 What is the observed value of the statistic W+ used for the test of hypotheses?…

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