Question 1

Answer the question.
-The average annual precipitation in Tewinville is 70 inches. In 2000, a particularly wet year, the precipitation was 140 inches. Which of the following statements are correct? More than one
Statement may be correct.
A: In 2000, the precipitation was 200% of normal.
B: In 2000, the precipitation was 100% of normal.
C: In 2000, the precipitation was 200% above normal.
D: In 2000, the precipitation was 100% above normal.

Accepted Answer

In 2000, the precipitation was 140 inches, which is double the average of 70 inches, making it 200% of normal (A). Saying it was 100% above normal (D) is another way of stating it doubled, as it was 100% more than the usual 70 inches.

Question 2

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described.
-The total number of cups of coffee drunk last year by Europeans.

Accepted Answer

The answer of Determine which of the numbers below is...

Question 3

Answer the question.
-Which of the statements below suggests an appropriate level of precision?

Accepted Answer

Typical bathroom scales do not measure weight with precision to the thousandth of a pound, making option D the most realistically precise measurement.

Question 4

Answer the question.
-Suppose that a test for a disease correctly gives positive results for 95% of those having the disease and correctly gives negative results for 90% of those who don't have the disease. Suppose also that
The incidence of the disease is 1%. If a person tests positive for the disease, what is the chance that
They have the disease? Find the exact percentage.

Accepted Answer

The answer of Answer the question.
-Suppose that a test for...

Question 5

Answer the question.
-Which of the statements below suggests an appropriate level of precision?

Accepted Answer

The number 8314 is precise and appropriate for counting people, as it does not round off to the nearest hundred or thousand and does not include a decimal, which would be inappropriate for counting whole people.

Question 6

Answer the question.
-In the 1980s, the population of Pleasanton decreased by 10%. In the 1990s, its population increased by 30%. How does the population of Pleasanton at the end of the 1990s compare with its
Population in 1980?

Accepted Answer

After a 10% decrease, the population is at 90% of its original level. A 30% increase on this reduced amount brings it to 117% of the original, hence a 17% increase overall.

Question 7

Solve the problem.
-The value of her house today is 400% more than when she bought it. Determine which of the statement's below is true.

Accepted Answer

If the value of her house today is 400% more than when she bought it, it means the value has increased by 4 times the original value, making it 5 times the original value in total.

Question 8

Solve the problem.
-Cathy scored 7 times as much as Helen on the test. Determine which of the statement's below is true.

Accepted Answer

If Cathy scored 7 times as much as Helen, then Cathy's score was 700% of Helen's score. This means Cathy's score is equal to Helen's score multiplied by 7 (100% original + 600% more = 700%).

Question 9

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described.
-The total number of breaths taken in his lifetime by a man who lives to be 80.

Accepted Answer

An average person breathes about 15 times per minute. Over a lifetime of 80 years (about 42,048,000 minutes), this would total around 630,720,000 breaths, which is closest to the order of magnitude of three hundred million.

Question 10

Solve the problem.
-John is 6 times as heavy as his dog. Determine which of the statement's below is true.

Accepted Answer

John weighs 500% more than his dog because if John's weight is 6 times his dog's weight, then he is 500% more than the dog's weight (since 6 times is 100% + 500% more).

Question 11

Answer the question.
-In 2000 a company increased its workforce by 60%. In 2001 it decreased its workforce by 60%. How does the size of its workforce at the end of 2001 compare with the size of the workforce at the
Beginning of 2000?

Accepted Answer

The workforce size at the end of 2001 is 36% lower than at the beginning of 2000. A 60% increase followed by a 60% decrease does not return to the original number because the decrease is from a larger base.

Question 12

Solve the problem.
-Allison weighs 29% less than she did one year ago. Determine which of the statement's below is true.

Accepted Answer

If Allison weighs 29% less than she did one year ago, she retains 100% - 29% = 71% of her weight from a year ago.

Question 13

Answer the question.
-A researcher looks at the percentage of people having high blood pressure amongst those who exercise regularly and amongst those who do not exercise regularly.
She selects 300 people under 40, of whom 200 exercise regularly and 100 do not. Among those who
Exercise regularly the rate of high blood pressure is 10% and among those who do not exercise
Regularly it is 15%.
She then selects 300 people over 40, of whom 100 exercise regularly and 200 do not. Among those
Who exercise regularly the rate of high blood pressure is 30% and among those who do not exercise
Regularly it is 35%.
However when she combines both age groups she finds that among those who exercise regularly
The rate of high blood pressure is 23.3% and among those who do not exercise regularly it is 21.6%.
Explain the apparent inconsistency in these results.

Accepted Answer

This is an example of Simpson's paradox, where a trend appears in several different groups of data but disappears or reverses when these groups are combined. In this case, within each age group, exercising seems to reduce the rate of high blood pressure, but when combining the data from both age groups, the overall rate of high blood pressure appears higher among those who exercise regularly. This is due to the different proportions of people in each age group and their respective rates of high blood pressure.

Question 14

Answer the question.
-Which of the statements below suggests an appropriate level of precision?

Accepted Answer

Estimating the number of people at a demonstration to the nearest thousand (120,000) provides a balance between accuracy and practicality, avoiding the false precision of exact counts in such contexts.

Question 15

Answer the question.
-In 2000, the balance on Martin's credit card increased by 50%. In 2001, the balance increased by 10%. How does the balance at the end of 2001 compare to the balance at the beginning of 2000?

Accepted Answer

The balance increased by 50% in 2000, and then that new total increased by an additional 10% in 2001. This results in a total increase of 65% over the original balance.

Question 16

Answer the question.
-In Slackville, the unemployment rate was 20% last year and this year it is 24%. Which of the following statements is correct?

Accepted Answer

The answer of Answer the question.
-In Slackville, the unemployment rate...

Question 17

Answer the question.
-Which of the statements below suggests an appropriate level of precision?

Accepted Answer

Statement B suggests an appropriate level of precision for everyday conversation or practical reporting, avoiding unnecessary detail while still being specific enough to be meaningful.

Question 18

Answer the question.
-Suppose that of the total amount collected in taxes by the U.S. government, 25% of it comes from families with incomes greater than $200,000.
If taxes are increased by 5% across the board, which of the following statements will be true?

Accepted Answer

Since the tax increase is applied across the board and families with incomes greater than $200,000 already contribute 25% of the total tax revenue, the proportion of additional revenue from these families will also be 25%, assuming the income distribution remains constant.

Question 19

Solve the problem.
-The retail cost of a computer is 22% more than its wholesale cost. Determine which of the statement's below is true.

Accepted Answer

If the retail cost is 22% more than the wholesale cost, it means you add 22% to the 100% of the wholesale cost, making it 122% of the wholesale cost.

Question 20

Answer the question.
-Any test for a disease has a certain rate of false positives (percentage of those who don't have the disease who test positive)and a certain rate of false negatives (percentage of those who do have the
Disease who test negative).
You would like to determine the chance that a person has the disease given that they have tested
Positive for the disease. Which of the following will you need to know?

Accepted Answer

To determine the chance that a person has the disease given they tested positive, you need the rate of false positives (to know how often the test incorrectly indicates disease), the rate of false negatives (to understand how often the test misses the disease), and the incidence of the disease in the population (to know the baseline rate of the disease). These factors together allow for the calculation of the probability of having the disease after a positive test result, using Bayes' theorem.

Quiz 3: Numbers in the Real World

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. -The total number of cups of coffee drunk last year by Europeans.

Answer the question. -Which of the statements below suggests an appropriate level of precision?

Answer the question. -Which of the statements below suggests an appropriate level of precision?

Answer the question. -In the 1980s, the population of Pleasanton decreased by 10%. In the 1990s, its population increased by 30%. How does the population of Pleasanton at the end of the 1990s compare with its Population in 1980?

Solve the problem. -The value of her house today is 400% more than when she bought it. Determine which of the statement's below is true.

Solve the problem. -Cathy scored 7 times as much as Helen on the test. Determine which of the statement's below is true.

Determine which of the numbers below is a possible order of magnitude estimate of the quantity described. -The total number of breaths taken in his lifetime by a man who lives to be 80.

Solve the problem. -John is 6 times as heavy as his dog. Determine which of the statement's below is true.

Answer the question. -In 2000 a company increased its workforce by 60%. In 2001 it decreased its workforce by 60%. How does the size of its workforce at the end of 2001 compare with the size of the workforce at the Beginning of 2000?

Solve the problem. -Allison weighs 29% less than she did one year ago. Determine which of the statement's below is true.

Answer the question. -Which of the statements below suggests an appropriate level of precision?

Answer the question. -In 2000, the balance on Martin's credit card increased by 50%. In 2001, the balance increased by 10%. How does the balance at the end of 2001 compare to the balance at the beginning of 2000?

Answer the question. -In Slackville, the unemployment rate was 20% last year and this year it is 24%. Which of the following statements is correct?

Answer the question. -Which of the statements below suggests an appropriate level of precision?

Answer the question. -Suppose that of the total amount collected in taxes by the U.S. government, 25% of it comes from families with incomes greater than $200,000. If taxes are increased by 5% across the board, which of the following statements will be true?

Solve the problem. -The retail cost of a computer is 22% more than its wholesale cost. Determine which of the statement's below is true.