Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
6th Edition
ISBN: 9780321914620
Author: Jeffrey O. Bennett, William L. Briggs
Publisher: PEARSON
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Chapter P, Problem 1DQ
To determine
Describe at least one way that mathematics is involved in each issue below.
Expert Solution & Answer
Explanation of Solution
Given:
Example: The spread of AIDS: Mathematics is used to study the probability of contracting AIDS.
- The long term viability of the Social Security system
- The appropriate level for the federal gasoline tax
- National health care policy
- Job discrimination against women or ethnic minorities
- Effects of population growth (or decline) on your community
- Possible bias in standardized tests (e.g., the SAT)
- The degree of risk posed by carbon dioxide emissions
- Immigration policy of the United States
- Violence in public schools
- Whether certain types of guns or ammunition should be banned
- An issue of your choice from today’s news
- The long-term viability of the Social Security system:
- The appropriate level for the federal gasoline tax:
- National health care policy:
- Job discrimination against women or ethnic minorities:
- Effects of population growth (or decline) on your community:
- Possible bias in standardized tests (e.g., the SAT):
- The degree of risk posed by carbon dioxide emissions:
- Immigration policy of the United States:
- Violence in public schools:
- Whether certain types of guns or ammunition should be banned:
- An issue of your choice from today’s news:
Mathematics is used to study of statistics of how long the Social Security system is capable.
Mathematics is used to study excise tax on gasoline per gallon.
Mathematics is used to study statistics of what type of health care policy required in the state.
Mathematics is used to study workplace gender discrimination in the country.
Mathematics is used to study fertility, mortality, and migration trends to make projection about population growth and decline.
Mathematics is used to study probability of the undeserved students who are getting admission through standardized tests.
Mathematics is used to study the probability of death cases due to carbon dioxide emissions.
Mathematics involved in this case calculating the total transit of people across its borders into the country, and we can calculate the total people who intend to work and who stay in the country.
Mathematics is used to study the probability of the students involved in the criminal activity.
Mathematics involved calculating the killing cases by certain types of guns or ammunition.
The news states “US has foolishly given Pakistan more than 33 billion dollars in aid over the last 15 years, and they have given us nothing but lies & deceit.”
Mathematics is used to study the total amount went to Pakistan for CSF (Coalition Support Funds) Reimbursement, Security related and Economic Related.
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Students have asked these similar questions
(b) An otherwise fair six-sided die has been tampered with in an attempt to
cheat at a dice game. The effect is that the 1 and 6 faces have a
different probability of occurring than the 2, 3, 4 and 5 faces.
Let θ be the probability of obtaining a 1 on this biased die. Then the
outcomes of rolling the biased die have the following probability mass
function.
Table 1 The p.m.f. of outcomes of rolls of a biased die
Outcome 1 2 3 4 5 6
Probability θ
1
4
(1 − 2θ)
1
4
(1 − 2θ)
1
4
(1 − 2θ)
1
4
(1 − 2θ) θ
(i) By consideration of the p.m.f. in Table 1, explain why it is
necessary for θ to be such that 0 < θ < 1/2. [2]
(ii) The value of θ is unknown. Data from which to estimate the value
of θ were obtained by rolling the biased die 1000 times. The result
of this experiment is shown in Table 2.
Table 2 Outcomes of 1000 independent rolls of a biased die
Outcome 1 2 3 4 5 6
Frequency 205 154 141 165 145 190
Show that the likelihood of θ based on these data is
L(θ) = C θ395 (1 − 2θ)
605
,…
Problem: The probability density function of a random variable is given by the exponential
distribution
Find the probability that
f(x) = {0.55e-0.55 x 0 < x, O elsewhere}
a. the time to observe a particle is more than 200 microseconds.
b. the time to observe a particle is less than 10 microseconds.
How to solve it explain it step by step please
Chapter P Solutions
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Ch. P - Prob. 1DQCh. P - Quantitative Concepts in the News. Identify the...Ch. P - Mathematics and the Arts. Choose a well-known...Ch. P - Quantitative Literature. Choose a favorite work of...Ch. P - Your Quantitative Major. Identify ways in which...Ch. P - Career Preparation. Realizing that Americans...Ch. P - Attitudes Toward Mathematics. What is your...Ch. P - "Bad at Math" as a Social Disease. Discuss reasons...
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