A social security Administration branch is considering the following two options for processing applications for social security cards. Option 1: Three clerks process applications in parallel from a single queue. Each clerk fills out the form for the application in the presence of the applicant. Processing time is exponential with a mean of 15 minutes. Ineterarrival times are exponential. Option 2: Each applicant first fills out an application wit

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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A manufacturer of exercise equipment knows that 15% of their products aredefective. They also know that only 35% of their customers will actually use the equipment in the first year after it is purchased. If there is a one-year warranty on the equipment, what proportion of the customers will actually make a valid warranty claim?
The Internal Revenue Service (IRS) provides a toll-free help line for taxpayers to call in and get answers to questions as they prepare their tax returns. In recent years, the IRS has been inundated with taxpayer calls and has redesigned its phone service as well as posted answers to frequently asked questions on its website (The Cincinnati Enquirer, January 7, 2010). According to a report by a taxpayer advocate, callers using the new system can expect to wait on hold for an unreasonably long time of 12 minutes before being able to talk to an IRS employee. Suppose you select a sample of 50 callers after the new phone service has been implemented; the sample results show a mean waiting time of 10 minutes before an IRS employee comes on the line. Based upon data from past years, you decide it is reasonable to assume that the standard deviation of waiting time is 8 minutes. Using your sample results, can you conclude that the actual mean waiting time turned out to be significantly less…
The Internal Revenue Service (IRS) provides a toll-free help line for taxpayers to call in and get answers to questions as they prepare their tax returns. In recent years, the IRS has been inundated with taxpayer calls and has redesigned its phone service as well as posting answers to frequently asked questions on its website (The Cincinnati Enquirer, January 7, 2010). According to a report by a taxpayer advocate, callers using the new system can expect to wait on hold for an unreasonably long time of 15 minutes before being able to talk to an IRS employee. Suppose you select a sample of 50 callers after the new phone service has been implemented; the sample results show a mean waiting time of 13 minutes before an IRS employee comes on line. Based upon data from past years, you decide it is reasonable to assume that the standard deviation of waiting times is 11 minutes. Use 0c = 0.05. What is the p-value (to 4 decimals)?
The Internal Revenue Service (IRS) provides a toll-free help line for taxpayers to call in and get answers to questions as they prepare their tax returns. In recent years, the IRS has been inundated with taxpayer calls and has redesigned its phone service as well as posting answers to frequently asked questions on its website (The Cincinnati Enquirer, January 7, 2010). According to a report by a taxpayer advocate, callers using the new system can expect to wait on hold for an unreasonably long time of 15 minutes before being able to talk to an IRS employee. Suppose you select a sample of 50 callers after the new phone service has been implemented; the sample results show a mean waiting time of 13 minutes before an IRS employee comes on line. Based upon data from past years, you decide it is reasonable to assume that the standard deviation of waiting times is 11 minutes. Use . 0.05. What is the P-Value?
The Internal Revenue Service (IRS) provides a toll-free help line for taxpayers to call in and get answers to questions as they prepare their tax returns. In recent years, the IRS has been inundated with taxpayer calls and has redesigned its phone service as well as posting answers to frequently asked questions on its website (The Cincinnati Enquirer, January 7, 2010). According to a report by a taxpayer advocate, callers using the new system can expect to wait on hold for an unreasonably long time of 15 minutes before being able to talk to an IRS employee. Suppose you select a sample of 50 callers after the new phone service has been implemented; the sample results show a mean waiting time of 13 minutes before an IRS employee comes on line. Based upon data from past years, you decide it is reasonable to assume that the standard deviation of waiting times is 11 minutes. Use a=0.05. A. State the hypotheses. null=_____. Ha=_____. B. what is the p-value (to 4 decimals)? _____. C. Using…
CWD Business systems maintains a successful Telecom sales department for Top up call creditin which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phonecalls to the department are answered automatically by an answering machine and asked to wait.As soon as the clerk is free, the party that has waited the longest is transferred and answered first.Calls come in at a rate of about 15 per hour. The clerk is capable of taking an order in an averageof 3 minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential.The clerk is paid $15 per hour, but because of lost goodwill and sales, CWD loses about $30 perhour of customer time spent waiting for the clerk to take an order. Part B CWD is considering adding a second clerk to take calls. The store would pay that person thesame $15 per hour.Using appropriate formula for the multiple channel model, answer the following questions. a. What is the probability that no customers are…
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Dave Fletcher, the general manager of North Carolina Engineering Corporation (NCEC), thinks that his firm’s engineer-ing services contracted to highway construction firms are directly related to the volume of highway construction business contractedwith companies in his geographic area. He wonders if this is reallyso, and if it is, can this information help him plan his operationsbetter by forecasting the quantity of his engineering servicesrequired by construction firms in each quarter of the year? Thefollowing table presents the sales of his services and total amountsof contracts for highway construction over the past eight quarters: a) Using this data, develop a regression equation for predictingthe level of demand of NCEC’s services. b) Determine the coefficient of correlation and the standard errorof the estimate.
Comcast Corporation is the largest cable television company, the second largest Internet service provider, and the fourth largest telephone service provider in the United States. Generally known for quality and reliable service, the company periodically experiences unexpectedservice interruptions. On January 14, 2014, such an interruption occurred for the Comcastcustomers living in southwest Florida. when customers called the Comcast office, a recordedmessage told them that the company was aware of the service outage and that it was anticipated that service would be restored in two hours. Assume that two hours is the mean time todo the repair and that the repair time has an exponential probability distribution.a. what is the probability that the cable service will be repaired in one hour or less?b. what is the probability that the repair will take between one hour and two hours?c. For a customer who calls the Comcast office at 1:00 p.m., what is the probability thatthe cable service…
The following question is on statistics. An automatic car wash takes exactly 5 minutes to wash a car. On average, 10 cars per hour arrive at the car wash. Suppose that 30 minutes before closing time, 5 cars are in line. If the car wash is in continuous use until closing time, is it likely anyone will be in line at closing time?