MATHEMATICAL EXCURSIONS>LL<
4th Edition
ISBN: 9780357097977
Author: Aufmann
Publisher: CENGAGE LEARNING (CUSTOM)
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 4.3, Problem 23ES
Football At the beginning of each football season, the coaching staff at Vista High School must vote to decide which players to select for the team. They use the weighted voting system {4: 3. 2. 1). In this voting system, the head coach. A. has a weight of 3, the assist ant coach. B. has a weight of 2, and the junior varsity coach. C. has a weight of I.
a. Compute the Banzhaf power index for each of the coaches.
b. Explaintiy it seems reasonable that the assisant coach and the junior varsity coach have the same Banzhaf power index in this voting system.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A fundraiser is offering a small gift to people making a donation. The donor can choose one of four gifts: a mug, a t-shirt, a plush toy, or a water bottle. The fundraiser would like to know if any of the gifts were more or less popular or were they equal in preference. The data for n = 40 donors are below:
A fundraiser is offering a small gift to people making a donation. The donor can choose one of four gifts: a mug, a t-shirt, a plush toy, or a water bottle. The fundraiser would like to know if any of the gifts were more or less popular or were they equal in preference. The data for n= 40 donors are below:
How many first place votes are needed for a majority?
Chapter 4 Solutions
MATHEMATICAL EXCURSIONS>LL<
Ch. 4.1 - Verify this apportionment using the Jefferson...Ch. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Prob. 3EECh. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Explain how to calculate the standard divisor of...Ch. 4.1 - Teacher Aides A total of 25 teacher aides are to...Ch. 4.1 - In the Hamilton apportionment method, explain how...Ch. 4.1 - Prob. 4ESCh. 4.1 - Governing Boards The following table shows how the...Ch. 4.1 - Forest Rangers The table below shows how the...
Ch. 4.1 - Sales Associates The table below shows the number...Ch. 4.1 - Hospital Interns The table below shows the number...Ch. 4.1 - House of Representatives The U.S. House of...Ch. 4.1 - College Enrollment The following table shows the...Ch. 4.1 - Medical Care A hospital district consists of six...Ch. 4.1 - What is the Alabama paradox?Ch. 4.1 - What is the population paradox?Ch. 4.1 - What is the new states paradox?Ch. 4.1 - 15. What is the Balinski-Young Impossibility...Ch. 4.1 - Apportionment of Projectors Consider the...Ch. 4.1 - Hotel Management A company operates four resorts....Ch. 4.1 - Prob. 18ESCh. 4.1 - Management Scientific Research Corporation has...Ch. 4.1 - Prob. 20ESCh. 4.1 - Elementary School Teachers The following table...Ch. 4.1 - Social Workers The following table shows the...Ch. 4.1 - Computer Usage The table below shows the number of...Ch. 4.1 - The population of Illinois increased by over...Ch. 4.1 - Prob. 25ESCh. 4.1 - Prob. 26ESCh. 4.1 - Computer Usage Use the Webster method to apportion...Ch. 4.1 - Demographics The table below shows the populations...Ch. 4.1 - Which of she following apportionment methods can...Ch. 4.1 - According to Michael Balinski and H. Peyton Young,...Ch. 4.1 - 31. What method is presently used to apportion the...Ch. 4.1 - Prob. 32ESCh. 4.1 - John Quincy Adams, the sixth president of the...Ch. 4.1 - In the Huntington-Hill method of apportionment,...Ch. 4.1 - Prob. 35ESCh. 4.2 - Using the Borda method of voting, which flavor of...Ch. 4.2 - Instead of using the normal Borda method, suppose...Ch. 4.2 - Prob. 3EECh. 4.2 - Suppose the Borda method used in Exercise I of...Ch. 4.2 - Prob. 5EECh. 4.2 - Can the assignment of points for first. Second,...Ch. 4.2 - Prob. 7EECh. 4.2 - Prob. 1ESCh. 4.2 - Explain why the plurality voting system may not be...Ch. 4.2 - Prob. 3ESCh. 4.2 - Explain how the plurality with elimination voting...Ch. 4.2 - Prob. 5ESCh. 4.2 - Prob. 6ESCh. 4.2 - Is there a best voting method? Is one method more...Ch. 4.2 - Explain why. if only two candidates are running,...Ch. 4.2 - Presidential Election The table below shows the...Ch. 4.2 - Breakfast Cereal Sixteen people were asked to rank...Ch. 4.2 - Cartoon Characters A kindergarten class was...Ch. 4.2 - Catering A 15-person committee is having lunch...Ch. 4.2 - Movies Fifty consumers were surveyed about their...Ch. 4.2 - Breakfast Cereal Use the Borda count method of...Ch. 4.2 - Prob. 15ESCh. 4.2 - Catering Use the Borda count method of voting to...Ch. 4.2 - Class Election A senior high school class held an...Ch. 4.2 - Cell Phone Usage A journalist reviewing various...Ch. 4.2 - Baseball Uniforms A Little League baseball team...Ch. 4.2 - Radio Stations A number of college students were...Ch. 4.2 - Class Election Use plurality with elimination to...Ch. 4.2 - Prob. 22ESCh. 4.2 - Campus Club A campus club has money left over in...Ch. 4.2 - Recreation A company is planning its annual summer...Ch. 4.2 - X-Men Movies Fans of the X-Men movies have been...Ch. 4.2 - Prob. 26ESCh. 4.2 - School Mascot A new college needs to pick a moscot...Ch. 4.2 - Election Five candidates are running for president...Ch. 4.2 - Prob. 29ESCh. 4.2 - Radio Stations Use the pairwise comparison method...Ch. 4.2 - Does the winner in Exercise tic satisfy the...Ch. 4.2 - 32. Does the winner in Exercise 12 satisfy the...Ch. 4.2 - Prob. 33ESCh. 4.2 - Prob. 34ESCh. 4.2 - Prob. 35ESCh. 4.2 - Prob. 36ESCh. 4.2 - Election Three candidates are running for mayor. A...Ch. 4.2 - Film Competition Three films have been selected as...Ch. 4.2 - 39. Election A campus club needs to elect four...Ch. 4.2 - Scholarship Awards The members of a scholarship...Ch. 4.2 - Another method of voting is to assign a weight. or...Ch. 4.2 - Prob. 42ESCh. 4.2 - Prob. 43ESCh. 4.3 - Using the data in Example 1 on page 211, list all...Ch. 4.3 - For the data in Example I on page 211, calculate...Ch. 4.3 - Prob. 3EECh. 4.3 - Prob. 4EECh. 4.3 - Create a voting system with three members that is...Ch. 4.3 - Prob. 6EECh. 4.3 - Prob. 7EECh. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - Prob. 3ESCh. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Prob. 8ESCh. 4.3 - Prob. 9ESCh. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Prob. 13ESCh. 4.3 - Prob. 14ESCh. 4.3 - Music Education A music department Consists of a...Ch. 4.3 - Prob. 16ESCh. 4.3 - Criminal Justice In a criminal trial, each of the...Ch. 4.3 - Criminal Justice In California civil court cases,...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Prob. 21ESCh. 4.3 - Prob. 22ESCh. 4.3 - Football At the beginning of each football season,...Ch. 4.3 - Prob. 24ESCh. 4.3 - Prob. 25ESCh. 4.3 - Prob. 26ESCh. 4.3 - Consider the weighted voting system { q:8,3,3,2 },...Ch. 4.3 - Prob. 28ESCh. 4.3 - Prob. 29ESCh. 4.3 - UN Security Council The United Nations C Security...Ch. 4 - Education The following table shows the...Ch. 4 - Airline Industry The following table shows the...Ch. 4 - Airline Industry The table below shows how the...Ch. 4 - 4. Education The following table shows the number...Ch. 4 - Technology A company has four offices. The...Ch. 4 - Automobile Sales Consider the apportionment of 27...Ch. 4 - Music Company MusicGalore.biz has offices in Los...Ch. 4 - Building Inspectors A city apportions 34 building...Ch. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Corporate Security The Huntington-Hill...Ch. 4 - Essay Contest Four finalists are competing in an...Ch. 4 - Ski Club A campus ski club is trying o decide...Ch. 4 - Prob. 14RECh. 4 - Consumer Preferences A group of consumers were...Ch. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Homecoming Queen Three high school students are...Ch. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - A weighted voting system for voters A. B. C. D....Ch. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - 25. Calculate the Banzhaf power indices for voters...Ch. 4 - Calculate the Banzhaf power indices for voters A,...Ch. 4 - Prob. 27RECh. 4 - Identify any dictator and all dummies for each...Ch. 4 - Four voters. A. B. C. and D. make decisions by...Ch. 4 - Postal Service The table below shows the number of...Ch. 4 - Computer Allocation The following table shows the...Ch. 4 - High School Counselors The following table shows...Ch. 4 - Prob. 4TCh. 4 - Consumer Preference One hundred consumers ranked...Ch. 4 - Prob. 6TCh. 4 - Exam Review A professor is preparing an extra...Ch. 4 - Prob. 8TCh. 4 - Drama Department The four staff members. A, B,C,...Ch. 4 - Three voters. A. B. and C, make decisions by using...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- The librarian at a public library wants to determine what proportion of the library users are children. The librarianhas a tally sheet on which she marks whether books are checked out by an adult or a child. She records this datafor every fourth patron who checks out books.e. A political party wants to know the reaction of voters to a debate between the candidates. The day after the debate,the party’s polling staff calls 1,200 randomly selected phone numbers. If a registered voter answers the phone oris available to come to the phone, that registered voter is asked whom he or she intends to vote for and whetherthe debate changed his or her opinion of the candidates.arrow_forwardThe College of Science surveys its graduating students to determine the starting salaries and the job market for the new graduates. The population of graduating students according to majors is recorded as follows: BS Bio (85), BSM- CS (102), BSM- BA (78), and BSM- AS (75). If you would like to select 100 samples, how large must a sample be for each major using proportionate allocation? Courses Number of Proportion Samples BS Biology students 85 BSM- CS 102 BSM- BA 78 BSM- AS 75 Total 100arrow_forwardIn a poll, 422 out of 1611 people said that their main satisfaction in life comes from work. Answer the question.arrow_forward
- One study of grand juries in Alameda County, California, compared the demographic characteristics of jurors with the general population, to see if the jury panels were representative.8 The results for age are shown below. The investigators wanted to know whether these 66 jurors were selected at random from the population of Alameda County. (Only persons 21 and over are considered; the county age distribution is known from Public Health Department data.) Fill out the last column below. All of your answers hould be accurate to the tenth digit, for example 4.8. The value of χ2 is [E]. Your answer should be an integer with no decimals. The degrees of freedom is [F]. Check that the p-value is essentially zero from the table. (True or False) With simple random sampling, it is almost impossible for a jury to differ this much from the county age distribution. The inference is that grand juries are not selected at random. Write true or false. [G]arrow_forwardOne study of grand juries in Alameda County, California, compared the demographic characteristics of jurors with the general population, to see if the jury panels were representative.8 The results for age are shown below. The investigators wanted to know whether these 66 jurors were selected at random from the population of Alameda County. (Only persons 21 and over are considered; the county age distribution is known from Public Health Department data.) Fill out the last column below. All of your answers hould be accurate to the tenth digit, for example 4.8. Age County-wide percentage number of jurors expected number of jurors 21 to 40 42 5 41 to 50 23 51 to 60 16 19 61 and over 19 33 Page 550 100 66 The value of x2 is Your answer should be an integer with no decimals. The degrees of freedom is Check that the p-value is essentially zero from the table. (True or False) With simple random sampling, it is almost impossible for a jury to differ this much from the county age distribution.…arrow_forwardTraffic department wants to know if automobile accident is a very serious problem in New York compared to other districts in US. Nine intersections in New York have been chosen at random. The number of accidents at those intersections has been recorded for three months. The average number of accidents at an intersection in US in the past three months is 3. The number of accidents at the chosen intersections in New York: A B C D E F G H I 6 8 7 4 8 7 7 11 5 Calculate the mean number of accidents in New York Calculate the sample standard deviation for the number of accidents in New York State the null hypothesis if traffic department wants to test whether automobile accident is a very serious problem in New York compared to other districts in US Continue from part c, state the corresponding alternative hypothesis of the test Continue from part c, calculate the test statistics of the test Continue from part e, what is the critical value of…arrow_forward
- A manufacturing plant makes computer chips 24 hours a day. Employees work one of three, 8 hour shifts during the morning (2am-10am), day (10am-6pm), and night (6pm-2am). Below are data on the number of defective chips on a randomly chosen 24 hour period. Shift Morning Day Night Number of Defective Chips 23 26 47 Total Chips Manufactured 330 330 330 The plant manager thinks there might be more defective computer chips manufactured during the night shift compared to the day shift. Give appropriate statistical evidence to test the managers' claim.arrow_forwardThe midterm grades of randomly picked eight students in an MMW class are as follows: 84, 90, 74, 84, 83, 89, 94, 79. What is the coefficient of variation? 6.608% 7.87% 84 2.50%arrow_forwardAt an art camp, students must specialize in one artistic medium. The camp director looked at her records to see which specialties students chose last summer. sculpture 11 metalworking 4 drawing 13 ceramics 12 Considering this data, how many of the next 50 students to sign up for camp this summer should you expect to specialize in ceramics?arrow_forward
- Out of 500 people in a room, 200 of them are wearing red shirts. Of the people wearing red shirts, 15% are wearing red pants. What percentage of the people in the room are wearing both red shirts and red pants?arrow_forwardOffice-chair racing is now an official sport in Japan. Teams of 3 race around a 200-meter circuit for 2 hours to see who can complete the most laps. Tonya, an office-chair racing coach, contacts the top 5 teams and randomly assigns them to complete a practice race using one of two popular brands of office chair: Brand A and Brand B. In a different time period, the same teams complete a practice race using the opposite brand of chair. Here are the data: A 2-column table with 5 rows. Column 1 is labeled Brand A with entries 116, 107, 101, 97, 94. Column 2 is labeled Brand B with entries 114, 102, 100, 94, 90. Calculate the mean difference (Brand A – Brand B) and the standard deviation of the differences.arrow_forwardsniparrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Finite Math: Markov Chain Example - The Gambler's Ruin; Author: Brandon Foltz;https://www.youtube.com/watch?v=afIhgiHVnj0;License: Standard YouTube License, CC-BY
Introduction: MARKOV PROCESS And MARKOV CHAINS // Short Lecture // Linear Algebra; Author: AfterMath;https://www.youtube.com/watch?v=qK-PUTuUSpw;License: Standard Youtube License
Stochastic process and Markov Chain Model | Transition Probability Matrix (TPM); Author: Dr. Harish Garg;https://www.youtube.com/watch?v=sb4jo4P4ZLI;License: Standard YouTube License, CC-BY