Math 2000 Midterm Exam

Spring 2001

Name: ___________________________________________________

This is a 75-minute open-book, open-notes exam. You must show all of your work clearly to receive full credit. Work six (6) of the following seven (7) problems and indicate which problems you wish to have graded.

1. Statistical studies. (15 points) Each month the Department of Labor surveys 60,000 households in the United States to determine various economic indicators. For example, based on this survey, the Department releases the monthly unemployment rate for the entire country, which is the percentage of eligible workers who are not employed.

a. What type of statistical study does the Department of Labor conduct?

b. What is the population for this statistical study?

c. What is the sample size for the study?

d. What is the sample statistic for the study?

e. What is the population parameter for the study?

f. The February 2001 unemployment rate was 4.2% with a margin of error of 0.2 percentage points. In what range (between what values) could you be confident that the true unemployment rate lies?

2. Units! (15 points) Assume the following currency exchange rates: 1 franc = $0.18, 1 punt (Irish) = $1.60.

a. Which is larger, one dollar or one punt? Explain.

b. How many francs are there in one dollar?

c. Suppose you see pears in a market priced at 6.25 francs per kilogram. What is the price in dollars per pound?

3. Percentages. (15 points)

a. Suppose there are 6 million unemployed people in a country and the unemployed rate is 4.2% (that is, 4.2% of all eligible workers are unemployed). How many eligible workers are there in the country?

b. From the New York Times: “On Friday, the Nasdaq stock exchange closed at 2,117, down 58% from 12 months ago.” At what level was the stock exchange 12 months ago?

4. Finance. (15 points) Robin starts paying $150 per month into a retirement account with an APR of 8.8%. What will the balance in the account be in 25 years? How much will she have deposited into the account? How much did she earn in interest? Assume monthly compounding.

5. U.S. age distribution. (15 points) The following graph shows the number of Americans in various age categories (using the left scale in units of millions of people). The graph also shows the percentage of Americans in those age categories (right scale). Notice that labels appear for every other age category.

a. Which age category has the most people? How many people?

b. How many Americans are over 80 years old (approximately)?

c. What percentage of Americans are under 24 years old (approximately)?

d. Complete the following sentence: The number of people under 5 years old is about ______ percent greater than the number of people between 65 and 69.

6. Birth rates. (15 points) In 1998, the highest and lowest birth rates in the United States were in Utah and Maine, respectively. Utah reported 46,128 births with a population of about 2.1 million people; Maine reported 13,530 births with a population of about 1.3 million.

a. Express the number of births in Utah in scientific notation.

b. How many people were born per day in Maine?

c. Find the annual birth rate in Utah in units of births per 1000 people in the population.

7. Venn diagrams. (15 points) Consider the Venn diagram below showing the reading preferences of the players on a rugby team. Please answer the following questions. It is important that you explain your reasoning for each answer.

a. How many players read fiction only?

b. How many players read poetry or non-fiction, but not fiction?

c. How many players read fiction and non-fiction, but not poetry?

d. How many players read poetry?