Math 2000 - Final Exam Practice Questions

Fall 2000

Important Dates

December 5 - Regular class period.

December 7 - Review session in class.

December 12, 12:30-2:30 - Final exam in the regular classroom.

Practice questions

This is not a practice exam, but a list of questions that are typical of final exam questions. You can check the course web page for old final exams.

1. The following table summarizes the results of a (hypothetical) study designed to determine whether drinking herbal tea prevents colds. Drinkers were participants who drank at least one cup of herbal tea per day for six weeks. The colds category consists of participants who contracted at least one cold during the six-week period.

	Drinkers	Non-drinkers
Cold	18	45
No cold	38	12

a. What percentage of tea drinkers contracted a cold? What percentage of people who got colds were non-drinkers?

b. What is the probability that a randomly selected participant contracted a cold?

c. What is the probability that a randomly selected participant is either a tea drinker or contracted a cold?

d. Draw a Venn diagram that summarizes the results of the study.

2. The graph below shows the death rates for four diseases since 1900 (in deaths per 100,000 people).

a. In what year (roughly) was the death rate due to cardiovascular disease the greatest? What was the death rate in that year (approximately)?

b. Describe the change in the death rate for tuberculosis since 1900.

c. In 2000, roughly how many Americans died of cancer?

3. What type of statistical study would be most appropriate to answer the following questions. Be as specific as possible. In each example, identify one possible source of bias and explain how you would avoid it.

a. To what political party do most auto mechanics belong?

b. Do side air bags in cars reduce fatalities?

4. In planning a 1500 mile trip, you want to compare the cost of air travel and car travel. Suppose that your car gets highway gas mileage of 33 miles per gallon and that you pay $1.60 per gallon of gasoline. In units of dollars per mile, compare the cost of driving to a $300 plane ticket.

5. Joan is in a 25% tax bracket and has a monthly take-home salary (after taxes) of $1800. What is her gross monthly salary (before taxes)?

6. “The Amazon River drains a sixth of the world’s run-off into the ocean. One day’s discharge at its mouth - 4.5 trillion gallons - could supply all U.S. households for five months.” (Quote from National Geographic, February 1995)

a. Express the daily discharge of the Amazon in scientific notation.

b. Given that 1 cubic foot = 7.5 gallons, what is the daily discharge in gallons?

c. What is the daily water use of U.S. households in gallons?

7. Explain whether the following statements describe exponential or linear growth.

a. The world population is increasing at a rate of 1.6% per year.

b. The population of Sioux City is increasing at a rate of 1200 people per year.

c. The speed of computers doubles every 5 years.

8. How many computer passwords with six symbols can be formed from the letters of the alphabet and the numerals 0 - 9?

9. How many different three-person subcommittees can be formed from a city council with 12 members?

10. How many ways can ten soccer teams be given a top five ranking?

11. If 3% of the student population is infected with flu, what are the chances that at least one of the first ten people you meet randomly has flu?

12. After 10 years, who will have a greater return on her investment: Alice, who invests $500 at an annual percentage rate (APR) of 5.2% with annual compounding or Brenda who invests $500 at an annual percentage rate (APR) of 5.0% with daily compounding?

13. Suppose you wish to accumulate $50,000 in an annuity (savings plan) over a period of 20 years. You would like to make monthly deposits and you find a plan that offers an annual percentage rate (APR) of 12% compounded monthly. How much should you deposit monthly in order to reach this goal?

Answers (not complete solutions)

1. a. 47.3%, 71.4%. b. 0.56. c. 0.89. One circle can represent either drinkers or non-drinkers; the other circle can represent either colds or no colds.

2. About 1970. Approximately 450 deaths per 100,000. b. The death rate decreased from about 200 deaths per 100,000 to zero. c. Approximately 540,000 deaths per year.

3. a. Observational; b. Observational, case-control.

4. Air cost is 20 cents per mile; car cost is 4.8 cents per mile.

5. $2400.

6. a. 4.5 ´ 10¹² gallons per day; b. 6 ´ 10¹¹ ft³ per day; c. 3 ´ 10¹⁰ gallons per day.

7. a. Exponential; b. Linear; c. Exponential.

8. 36⁶ = 2,176,782,336 passwords.

9. ₁₂C₃ = 220.

10. ₁₀P₅ = 30,240.

11. P = 0.26 = 26%.

12. Alice: $830.09, Brenda: $824.33.

13. $50.54.