A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephonelines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents whoattempt to use the system when it is full are denied access; no waiting is allowed.Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well asannoying for agents. Access requests follow a Poisson probability distribution, with a mean of 37 calls per hour. The service rate per line is 22 calls per hour.(a) What is the probability that 0, 1, 2, and 3 access lines will be in use? (Round your answers to four decimal places.)P(0) = 0.1642P(1) = 0.2911P(2) = 0.2572P(3) = 0.1521XXXX(b) What is the probability that an agent will be denied access to the system? (Round your answers to four decimal places.)P = 0.1521kX(c) What is the average number of access lines in use? (Round your answers to two decimal places.)0.56X(d) In planning for the future, management wants to be able to handle45 calls per hour. In addition, the probability that an agent will be denied access to the system shouldbe no greater than the value computed in part (b). How many access lines should this system have?4=

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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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please help with 3, 4, and 5 High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges reject more early applicants. Suppose that for a recent admissions class, an Ivy League college received 2851 applications for early admission. Of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. Answer questions 3-5. 3.Use the data to estimate P(E), P(R),…
An inventor has developed a system that allows visitors to museums, zoos, and other attractions to get information at the touch of a digital code. For example, zoo patrons can listen to an announcement (recorded on a microchip) about each animal they see. It is anticipated that the device would rent for $3.00 each. The installation cost for the complete system is expected to be about $400,000. The Milwaukee Zoo is interested in having the system installed, but management is uncertain about whether to take the risk. A financial analysis of the problem indicates that if more than 10% of the Zoo visitors rent the system the zoo will make a profit. To help make the decision, a sample of 400 zoo visitors is given details of the system’s capabilities and cost. Forty eight people say they would rent the device. c). Estimate the actual percentage of the visitors who would rent the system using a 98% confidence interval using Minitab.
Hillary and Adams, Inc., is a privately owned firm located in Atlanta that serves as the regional distributor of natu-ral food products for Georgia, Kentucky, North Carolina, South Carolina, and Tennessee. They are particularlywell known for their unique blend of fiery hot Habanera sauces. Every week, a truck leaves the large distributioncenter in Atlanta to stock local warehouses located in Charlotte, North Carolina; Charleston, South Carolina;Columbia, South Carolina; Knoxville, Tennessee; Lexington, Kentucky; and Raleigh, North Carolina. The truckvisits each local warehouse only once and returns to Atlanta after all the deliveries have been completed. Thedistance between any two cities in miles is given below John Jensen, vice president of logistics at Hillary and Adams, Inc., is worried about the rising fuel costs.With a reduction in operating budgets, he is interested in finding a route that would minimize the distance trav-eled by the truck.Use the NN heuristic to identify a…
According to Wikipedia, Marie Skłodowska Curie (7 November 1867 - 4 July 1934) was a Polish and naturalized-French physicist and chemist who conducted pioneering research on radioactivity. She was the first woman to win a Nobel Prize, the first person and the only woman to win the Nobel Prize twice, and the only person to win the Nobel Prize in two different scientific fields. She was part of the Curie family legacy of five Nobel Prizes. She was also the first woman to become a professor at the University of Paris, and in 1995 became the first woman to be entombed on her own merits in the Panthéon in Paris. Madame Curie died 1934 from aplastic anaemia, a rare condition linked to high levels of exposure to the radioactive elements polonium and radium. Due to her many years of exposure to these radioactive. elements, her remains are dangerously radioactive and are entombed in a lead-lined coffin in France's Panthéon. The thick lead shields visitors to the Panthéon from the dangerous…
A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed. Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with a mean of 33 calls per hour. The service rate per line is 22 calls per hour. (a) What is the probability that 0, 1, 2, and 3 access lines will be in use? (Round your answers to four decimal places.) P(0) = 0.2388 P(1) = 0.3582 P(2) = 0.2687 P(3) = 0.1343 (b) What is the probability that an agent…
Consider a remote town in which two restaurants, All-You-Can-Eat Café and GoodGrub Diner, operate in a duopoly. Both restaurants disregard health and safety regulations, but they continue to have customers because they are the only restaurants within 80 miles of town. Both restaurants know that if they clean up, they will attract more customers, but this also means that they will have to pay workers to do the leaning. If neither restaurant cleans, each will earn $14,000; alternatively, if they both hire workers to clean, each will earn only $11,000. However, if one cleans and the other doesn't, more customers will choose the cleaner restaurant; the cleaner restaurant will make $18,000, and the other restaurant will make only $6,000. Complete the following payoff matrix using the information just given. (Note: All-You-Can-Eat Café and GoodGrub Diner are both profit-maximizing firms.) All-You-Can-Eat Café $ Cleans Up Doesn't Clean Up $ Cleans Up $ 81°F Sunny $ GoodGrub Diner $ $ If…
A real estate investment trust (REIT) owns first-class office properties in selected markets. According to its website, the occupancy rates last year for its holdings in four major cities are available below. Complete parts a through c below.
A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed. Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with a mean of 33 calls per hour. The service rate per line is 22 calls per hour. (a) What is the probability that 0, 1, 2, and 3 access lines will be in use? (Round your answers to four decimal places.) P(0) P(1) P(2) P(3) = = = (b) What is the probability that an agent will be denied access to the…
An automobile company produces cars in Los Angeles and Detroit and has a warehouse in Atlanta.The company supplies cars to customers in Houston and Tampa. The costs of shipping a car betweenvarious points are listed in the table below, where a blank means that a shipment is not allowed. LosAngeles can produce up to 1100 cars, and Detroit can produce up to 2900 cars. Houston must receive2400 cars, and Tampa must receive 1500 cars. (Include your formulations to receive credit. Thinkcarefully about the transhipment locations.) (a) Determine how to minimize the cost of meeting demands in Houston and Tampa. (b) Modify the answer to part (a) if shipments between Los Angeles and Detroit are not allowed. (c) Modify the answer to part (a) if shipments between Houston and Tampa are allowed at a cost of$5 per car.
The department of code enforcement of a country government issues permits to general contractors to work on residential projects. For each permit issued, the department inspects the result of the project and gives a "pass" or "fail" rating. A failed project must be re-inspected until it receives a pass rating. The department had been frustrated by the high cost of re-inspection rate and decided to publish the inspection records of all contractors on the web. It was hoped that public access to the records would lower the re-inspection rate. A year after the web access was made public, two samples of records were randomly selected. One sample was selected from the pool of records before web publication and one after. The proportion of projects that passed on the first inspected was noted for each sample. The results are summarized below. No Public Web Access nį = 500, ĝ1 = 0.67 Public Web Access n2 = 100, p2 = 0.80 A test, at a 0.10 level of significance, is to be conducted as to whether…
Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each section of Finite Math has 40 students and earns the college $40,000 in revenue. Each section of Applied Calculus has 40 students and earns the college $60,000, while each section of Computer Methods has 10 students and earns the college $28,000. Assuming the college wishes to offer a total of seven sections, accommodate 220 students, and bring in $296,000 in revenues, how many sections of each course should it offer?

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