USING + UNDERSTANDING MATH CUSTOM
USING + UNDERSTANDING MATH CUSTOM
6th Edition
ISBN: 9780137721023
Author: Bennett
Publisher: PEARSON C
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Chapter P, Problem 1DQ
To determine

Describe at least one way that mathematics is involved in each issue below.

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Given:

Example: The spread of AIDS: Mathematics is used to study the probability of contracting AIDS.

  1. The long term viability of the Social Security system
  2. The appropriate level for the federal gasoline tax
  3. National health care policy
  4. Job discrimination against women or ethnic minorities
  5. Effects of population growth (or decline) on your community
  6. Possible bias in standardized tests (e.g., the SAT)
  7. The degree of risk posed by carbon dioxide emissions
  8. Immigration policy of the United States
  9. Violence in public schools
  10. Whether certain types of guns or ammunition should be banned
  11. An issue of your choice from today’s news
  1. The long-term viability of the Social Security system:
  2. Mathematics is used to study of statistics of how long the Social Security system is capable.

  3. The appropriate level for the federal gasoline tax:
  4. Mathematics is used to study excise tax on gasoline per gallon.

  5. National health care policy:
  6. Mathematics is used to study statistics of what type of health care policy required in the state.

  7. Job discrimination against women or ethnic minorities:
  8. Mathematics is used to study workplace gender discrimination in the country.

  9. Effects of population growth (or decline) on your community:
  10. Mathematics is used to study fertility, mortality, and migration trends to make projection about population growth and decline.

  11. Possible bias in standardized tests (e.g., the SAT):
  12. Mathematics is used to study probability of the undeserved students who are getting admission through standardized tests.

  13. The degree of risk posed by carbon dioxide emissions:
  14. Mathematics is used to study the probability of death cases due to carbon dioxide emissions.

  15. Immigration policy of the United States:
  16. 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.

  17. Violence in public schools:
  18. Mathematics is used to study the probability of the students involved in the criminal activity.

  19. Whether certain types of guns or ammunition should be banned:
  20. Mathematics involved calculating the killing cases by certain types of guns or ammunition.

  21. An issue of your choice from today’s news:
  22. 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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(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.
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