Mathematics: A Practical Odyssey
8th Edition
ISBN: 9781305104174
Author: David B. Johnson, Thomas A. Mowry
Publisher: Cengage Learning
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Chapter 6.CR, Problem 8CR
To determine
To apportion:
The legislative seats by Hamilton’s method.
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1. World's Richest. Each year, Forbes magazine publishes a list of the world's richest people. In
2009, the six richest people, their citizenship, and their wealth (to the nearest billion dollars)
Wealth ($ billion)
Citizenship
United States
Name
Willlam Gate (G)
Warren Buffett (B)
Carlos Slim Helu (H)
40
United States
38
Мexico
35
United States
Lawrence Ellison (E)
Karl Albrecht (A)
23
Sweden
22
Ingvar Kamprad (K)
Germany
22
a. Calculate the mean wealth, µ, of the six people.
For samples of size 2, construct a table and calculate the means for samples of size 2.
c. For a random sample of size 2, what is the chance that the sample mean will equal the
population mean?
d. For a random sample of size 2, determine the probability that the mean wealth of the two
people obtained will be within 2 (i.e., $2 billion) of the population mean. Interpret your result in
terms of percentages.
b.
please help me fast....
The Republic of Tropicana is a small country consisting of five states (A, B, C, D, and E). The total population of Tropicana is 27.4 million. According to the Tropicana constitution, the seats in parliament (i.e. the legislature) are apportioned to the states according to their population. The table below shows each state's standard quota
A
B
C
D
E
Standard Quota
41.2
31.9
24.8
22.6
16.5
(a) Find the number of seats in the Tropicana Legislature: Answer
(b) Find the standard divisor: Answer
(c) Find the population of each state and fill in the table below. (Hint: Write the equation for the standard divisor. Can you use it to find populations?)
A
B
C
D
E
Population
Answer
Answer
Answer
Answer
Answer
(d) Find the apportionment under Adam's method of the republic of Tropicana parliament (i.e. legislature). (Hint: Look for suitable divisors in the interval 205,000 to 206,000.)
A gets Answer seats, B…
Chapter 6 Solutions
Mathematics: A Practical Odyssey
Ch. 6.1 - Four candidates, Alliotti, Baker, Cruz, and Daud,...Ch. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.1 - Number of Ballots Cast 6 8 7 10 15 1st choice C C...Ch. 6.1 - Prob. 9ECh. 6.1 - Prob. 10E
Ch. 6.1 - Prob. 11ECh. 6.1 - Four candidates, Harrison H, Lennon L, McCartney...Ch. 6.1 - Prob. 13ECh. 6.1 - Five candidates, Fino F, Gempler G, Holloway H,...Ch. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - In an election, there are seven candidates. a....Ch. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - What is Arrows Impossibility Theorem?Ch. 6.2 - A small country consists of three states, A, B and...Ch. 6.2 - A small country consists of three states, A, B and...Ch. 6.2 - Suppose that the governors of three Middle...Ch. 6.2 - Suppose that the governors of three midwestern...Ch. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - A local school district contains four middle...Ch. 6.2 - A local school district contains four elementary...Ch. 6.2 - Prob. 11ECh. 6.2 - In J.R.R. Tolkiens Middle Earth, the regions in...Ch. 6.2 - Prob. 13ECh. 6.2 - Prob. 14ECh. 6.2 - Prob. 15ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Prob. 18ECh. 6.2 - Prob. 19ECh. 6.2 - Prob. 20ECh. 6.2 - Prob. 21ECh. 6.2 - Prob. 22ECh. 6.2 - Prob. 23ECh. 6.2 - Prob. 24ECh. 6.2 - Prob. 25ECh. 6.2 - Prob. 26ECh. 6.2 - Prob. 27ECh. 6.2 - Prob. 28ECh. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Prob. 31ECh. 6.2 - Prob. 32ECh. 6.2 - Use the Hill-Huntington Method to determine how...Ch. 6.2 - Prob. 34ECh. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - Prob. 39ECh. 6.2 - Prob. 40ECh. 6.2 - Prob. 41ECh. 6.2 - Prob. 42ECh. 6.2 - Prob. 43ECh. 6.2 - Prob. 44ECh. 6.2 - Prob. 45ECh. 6.2 - Prob. 46ECh. 6.2 - Prob. 47ECh. 6.2 - Prob. 48ECh. 6.2 - What is apportionment?Ch. 6.2 - Prob. 50ECh. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Prob. 53ECh. 6.2 - Prob. 54ECh. 6.2 - Prob. 55ECh. 6.2 - Prob. 56ECh. 6.2 - Prob. 57ECh. 6.2 - Since the founding of the United States, what...Ch. 6.2 - Prob. 59ECh. 6.2 - Prob. 60ECh. 6.3 - A small country consists of three states: A, B,...Ch. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - A small country consists of four states: A, B, C,...Ch. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Prob. 10ECh. 6.3 - A small country consists of three states:A, B, and...Ch. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - What is the Alabama Paradox? Explain its meaning.Ch. 6.3 - Prob. 17ECh. 6.3 - Prob. 18ECh. 6.3 - Prob. 19ECh. 6.CR - Prob. 1CRCh. 6.CR - Prob. 2CRCh. 6.CR - Prob. 3CRCh. 6.CR - Prob. 4CRCh. 6.CR - Prob. 5CRCh. 6.CR - Prob. 6CRCh. 6.CR - Prob. 7CRCh. 6.CR - Prob. 8CRCh. 6.CR - Prob. 9CRCh. 6.CR - Prob. 10CRCh. 6.CR - Prob. 11CRCh. 6.CR - Prob. 12CRCh. 6.CR - Prob. 13CRCh. 6.CR - Prob. 14CRCh. 6.CR - Prob. 15CRCh. 6.CR - Prob. 16CRCh. 6.CR - Prob. 17CRCh. 6.CR - A small country consists of three states: A, B,...Ch. 6.CR - Prob. 19CRCh. 6.CR - Prob. 20CRCh. 6.CR - Prob. 21CRCh. 6.CR - Prob. 22CRCh. 6.CR - Prob. 23CRCh. 6.CR - Prob. 24CRCh. 6.CR - Prob. 25CRCh. 6.CR - Prob. 26CRCh. 6.CR - Prob. 27CRCh. 6.CR - Prob. 28CRCh. 6.CR - What is the New States Paradox? Explain its...Ch. 6.CR - Prob. 30CRCh. 6.CR - Prob. 31CRCh. 6.CR - Prob. 32CRCh. 6.CR - Prob. 33CRCh. 6.CR - Prob. 34CRCh. 6.CR - What method of appointment for the House of...
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- 1. World's Richest. Each year, Forbes magazine publishes a list of the world's richest people. In 2009, the six richest people, their citizenship, and their wealth (to the nearest billion dollars) Name Citizenship Wealth ($ billion) Willlam Gate (G) Warren Buffett (B) Carlos Slim Helu (H) Lawrence Ellison (E) Karl Albrecht (A) United States 40 United States 38 Мexico 35 United States 23 Sweden 22 Ingvar Kamprad (K) Germany 22 Calculate the mean wealth, µ, of the six people. а. b. For samples of size 2, construct a table and calculate the means for samples of size 2. С. For a random sample of size 2, what is the chance that the sample mean will equal the population mean? d. For a random sample of size 2, determine the probability that the mean wealth of the two people obtained will be within 2 (i.e., $2 billion) of the population mean. Interpret your result in terms of percentages.arrow_forwardTwo nurses at Northwood Hospital’s Cardiac Care Unit are assigned to care for eight patients. Nurses are responsible for administering medication, taking vital signs, and responding to frequent calls for assistance that can come either from the patient, or the equipment monitoring the patient’s current condition. On an average, each patientrequires attention three times each hour. Nurses average 6 minutes per patient visit.a. What is the average utilization of the nursing staff?b. On an average, how many patients are waiting for a nurse?c. By how much would adding a third nurse reduce the patient waiting time?arrow_forwardTwenty sections of bilingual math courses, taught in both English and Spanish, are to be offered in introductory algebra, intermediate algebra, and liberal arts math. The preregistration figures for the number of students planning to enroll in these bilingual sections are given in the following table. Use Webster's method with d = 29.6 to determine how many bilingual sections of each course should be offered. Course Introductory Algebra Intermediate Algebra Liberal Arts Math Enrollment 139 271 182 ..... Course Introductory Algebra Number of Apportioned Sections (Type an integer.) Course Intermediate Algebra Number of Apportioned Sections 9 (Type an integer.) Course Liberal Arts Math Number of Apportioned Sections (Type an integer.)arrow_forward
- 12. Four academic areas at a college have 500 students and want to form a 25-member committee apportioned according to the number of students in each area. Complete the chart to find Hamilton's apportionment. Academic Education Business Music Psychology Area # of Students 165 139 67 129 Result of Division 8.25 6.95 3.35 6.45 Std Quota 8. Hamiltonarrow_forward3. Please use the table below as reference. State New York Pennsylvania Kentucky Vermont Louisiana Population 1,918,608 1,348,233 687,917 280,652 215,739 a. Find the modified quota for each park using the divisor 49,800.arrow_forwardUse Webster's method of apportionment to solve the following problem. 2. Suppose a nation has 5 states, with populations shown in the chart below. The representative body had 150 seats. Find: the standard divisor, the modified divisor, and the distribution of representatives to each state. Then complete the table. Round all standard and modified quotas to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator. Representative Seats 150 State Population Standard Rounded Modified Modified Quotas Quotas Quotas Rounded Quotas A 1,895,500 1,234,500 845,200 В C 399,120 500,680 4,875,000 D E Total Standard Divisor Modified Divisorarrow_forward
- 9. A grant and a newly passed levy will allow a county to buy 13 new fire trucks for its fire precincts. The new trucks are going to be allotted to the precincts based on the number of times each precinct had to respond to calls in the last six months. Use the Hamilton Apportionment Plan and the table below to determine the number of fire trucks each precinct will receive. District Number of Calls D-1 45 D-2-1 73 D-2-2 100 D-3 67 D-4-1 179 D-4-2 95arrow_forwardSuppose that the governors of three midwestern region states have agreed to form an interstate bureau to foster historical awareness, tourism, and commerce. The bureau will have ten seats, and the populations of the states are given in the figure shown below. Use Hamilton's Method to apportion the bureau seats. State A B C Population 9,938,480 5,363,704 4,819,485 Seatsarrow_forwardUse Webster's method of apportionment to solve the following problem. 2. Suppose a nation has 5 states, with populations shown in the chart below. The representative body had 150 seats. Find: • the standard divisor, the modified divisor, and • the distribution of representatives to each state. Then complete the table. Round all standard and modified quotas to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator. Representative Seats State A B C Total Standard Divisor Modified Divisor 150 Population 1,895,500 1,234,500 845,200 399.120 500.680 4,875,000 Standard Rounded Modified Modified Quotas Quotas Rounded Quotas Quotasarrow_forward
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