A low-cost airline currently checks itspassengers using two desks and a Maitred'Hotel queuing system. Passengers arriveaccording to a Poisson process with a meanrate of 35 per hour, and the check in time ateither desk is negatively exponentiallydistributed with a mean time of 3.2 minutesper passenger. The airline is consideringimplementing a new system which isexpected to halve the mean check-in timewhilst also making the process less variableso that the standard deviation of check intimes will be only 0.6 minutes. The airline'smanagement is hoping that, with the newsystem, they will be able to use only onecheck-in desk. Carry out an investigation toenable you to advise them on whether thisis likely to be correct and also on how theaverage queue length will be affected bythis proposed change.

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Answered: A low-cost airline currently checks its…

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 3.5 accidents per year. Find the mean waiting time between accidents. year
A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the pack-ages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051 ounce. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.05 level of significance.) Determine the p- value and interpret its meaning.
A researcher wants to determine if exposure to subliminal (unconscious) images depicting older adults (80-95 years old) will influence the time it takes pedestrians to get across a busy intersection using a crosswalk. A random sample of sixty pedestrians are exposed to a set of subliminally presented positive images using a special electronic traffic signal before the signal prompts them to cross. From previous studies (using the same crosswalk and intersection), the experimenter knows that when no subliminal images are presented, the average time it takes the city’s population to cross is 30.5 seconds, with a standard deviation = 5.5 seconds.
A SimAirlines aircraft that flies between BWI and San Diego airport has 100 seats, and there are two types of fares: full ($500) and discount ($300). Although there is an unlimited demand for the discount fare, demand for the full fare is estimated to be normally distributed with mean 24 seats and standard deviation 16 seats. To maximize the revenue generated from this flight, how many seats SimAirlines should protect for full-fare passengers?
A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of eight ounces of coffee per cup. If it dispenses more than that on average, the corporation may lose money, and if it dispenses less, the customers may complain.BIG Corporation would like to estimate the mean amount of coffee, μ, dispensed per cup by this machine. BIG will choose a random sample of cup amounts dispensed by this machine and use this sample to estimate μ. Assuming that the standard deviation of cup amounts dispensed by this machine is 0.35 ounces, what is the minimum sample size needed in order for BIG to be 90% confident that its estimate is within 0.08 ounces of μ? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).
A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of eight ounces of coffee per cup. If it dispenses more than that on average, the corporation may lose money, and if it dispenses less, the customers may complain. BIG Corporation would like to estimate the mean amount of coffee, μ, dispensed per cup by this machine. BIG will choose a random sample of cup amounts dispensed by this machine and use this sample to estimate μ. Assuming that the standard deviation of cup amounts dispensed by this machine is 0.43 ounces, what is the minimum sample size needed in order for BIG to be 90% confident that its estimate is within 0.08 ounces of μ? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).
A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of eight ounces of coffee per cup. If it dispenses more than that on average, the corporation may lose money, and if it dispenses less, the customers may complain.BIG Corporation would like to estimate the mean amount of coffee, , dispensed per cup by this machine. BIG will choose a random sample of cup amounts dispensed by this machine and use this sample to estimate . Assuming that the standard deviation of cup amounts dispensed by this machine is 0.35 ounces, what is the minimum sample size needed in order for BIG to be 90% confident that its estimate is within 0.08 ounces of ?
A national research group reported that 36% of 18-24 year olds watch a cable news channel regularly. The director of media relations at a large university wanted to know what proportion of students at her university who watch a cable news channel regularly. If it is less than 36%, then she will unsubscribe to the news channels. She sampled 200 random students and found that 63 watched cable news regularly. Should she conclude that proportion of students at her university who watch cable news regularly is less than 36% at the 8% significance level? In the context of this problem and your conclusion, what type of error is possible? In the context of this problem, what would the error be? In the context of this problem, what would be a possible consequence of this error?
Through an interaction with pregnant mothers, a researcher noticed that long waitinghours could be a reason for most mothers not attending Antenatal Care (ANC) atIHK. To further investigate this claim, a researcher recorded reporting time andleaving time of all 150 mothers who had come for ANC at IHK from 11th to 15thSeptember 2014. He calculated the mean waiting time as 67 minutes with a standarddeviation of 63 minutes. In the study, he assumed a 95% level of confidence. b. It will take between 50 and 75 minutes to attend to pregnant motherc) After the analysis, the researcher concluded that mothers who spent aminimum of 80 minutes at the IHK ANC clinic were more dissatisfied thanmothers who spent less than 80 minutes. Test the validity of this claim andstate the type I error
A newly hired human resource analyst proposes to senior management that the number of employee sick days could be reduced by converting to a flex-time work schedule. Assume that historical records show that the population mean for employee sick days is 5.28 days with a population standard deviation of 2.14 days. Senior management agrees to a one-year pilot study involving fifty employees working a flex-time schedule. After one-year, the analyst reports to management that the fifty employees in the study averaged 4.68 sick days during the year. Does the flex-time work schedule reduce employee sick days? What are the appropriate null and alternative hypotheses for this study? Assuming that the H0 is true, what is the probability of the analyst arriving at these results? (i.e., what is the p-value?) Does the flex-time work schedule reduce employee sick days? Using a 0.05 level of significance, what is the necessary value of the test statistic to justify rejecting…
Suppose that the talk time on a fully charged iPhone is approximately normally distributed with mean 7 hours and standard deviation 0.8 hour? (a) What is the probabilitiy that a fully charged iPhone will last less than 6 hours?
A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in New York and Illinois. Due to recent trends in the childcare industry, the firm suspects that the that the mean annual income of childcare workers in the state of New York is greater than the mean annual income of childcare workers in Illinois. To see if this is true, the firm selected a random sample of 20 childcare workers from New York and an independent random sample of 20 childcare workers from Illinois and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars New York 46686 , 34979 , 47325 , 48892 , 51128 , 56792 , 47785 , 48995 , 57301 , 55176 , 48002 , 45718 , 50351 , 58527 , 47067 , 53699 , 54361 , 49727 , 36426 , 50870 Illinois 48009 , 46871 , 42774 , 49790 , 43163 , 45401 , 41068 , 50300 , 47064 , 42003 , 47775 , 41917…

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