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MTH 216 Week 1 Checkpoint

Decide whether the statement below makes sense (or is clearly true) or does not make sense (or is clearly false). Explain.

In my experimental study, I used a sample that was larger than the population.

A.

No, the statement does not make sense. The sample size should always equal the population size.

B.

Yes, the statement makes sense. A sample is always larger than the population.

C.

No, the statement does not make sense. A sample is a subset of the population and cannot be larger than the population.

D.

Yes, the statement makes sense. A sample can be as large as desired.

Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.

I wanted to test the effects of vitamin C on colds, so I gave the treatment group vitamin C and gave the control group vitamin D.

A.

The statement does not make sense. The control group should only receive a placebo, not another treatment.

B.

The statement makes sense. The treatment and control groups are receiving different treatments.

C.

The statement does not make sense. The vitamin C should be given to the control group, not the treatment group.

D.

The statement makes sense. The experiment has both a control group and a treatment group.

Identify any potential sources of bias in the following study.

An exit poll designed to predict the winner of a local election uses interviews

with every

Republican nbsp

who

and 11 : 00

a.m.

What sources of bias, if any, might this study have?

A.

Selection bias only

B.

Participation bias only

C.

Both selection and participation bias

D.

There is probably no bias in the study.

Discuss the differences between the following questions, each of which could be the basis for a statistical study.

bullet

What percentage of Internet dates lead to marriage?

bullet

What percentage of marriages begin with Internet dates?

A.

The questions are too different to compare.

B.

The questions have different populations.

C.

The percentage of marriages beginning with Internet dates would be an observation while the percentage of Internet dates that lead to marriage would be an experiment.

D.

The percentage of marriages beginning with Internet dates can be accurately measured while the percentage of Internet dates that lead to marriage cannot be accurately measured.

The stacked line chart shows the numbers of college degrees awarded to men and women over time.

19001920194019601980200020040060080010001,2001,400

A stacked line chart has its horizontal axis labeled “Year” from 1900 to 2000 in increments of 5 and its vertical axis labeled “College graduates (hundred thousands)” from 0 to 14 in increments of 1. The area between the bottom line and the horizontal axis is shaded blue; the area between the top line and bottom line is shaded pink. The data for the bottom line are approximated as follows: 1900, 0.25; 1910, 0.25; 1920, 0.5; 1930, 0.75; 1940, 1; 1950, 3.75; 1960, 3; 1970, 5.25; 1980, 6.5; 1990, 5.75; 2000, 5. The data for the top line are approximated as follows: 1900, 0.25; 1910, 0.5; 1920, 0.75; 1930, 1.25; 1940, 1.75; 1950, 4.5; 1960, 3.75; 1970, 9; 1980, 10.5; 1990, 11.25; 2000, 11.75.

A legend shows that the color blue represents “Men” and the color pink represents “Women.” MenWomen

a. Estimate the numbers of college degrees awarded to men and to women (separately) in 1930 and in 1990.

The number of college degrees awarded to men in 1930 was

75 comma 000

.

The number of college degrees awarded to women in 1930 was

50,000

.

The number of college degrees awarded to men in 1990 was

569,500

.

The number of college degrees awarded to women in 1990 was

548,500

.

b. Compare the numbers of degrees awarded to men and to women (separately) in 1980 and 2000. Choose the correct answer below.

A.

In 1980, more men than women received degrees; in 2000, more women than men received degrees.

B.

In 1980 and in 2000, the number of men and women who received degrees were the same.

C.

In 1980, more women than men received degrees; in 2000, more men than women received degrees.

c. During what decade did the total number of degrees awarded increase the most?

A.

1990s

B.

1940s

C.

1920s

D.

1960s

d.

Compare the total numbers of degrees awarded in 1950 and 2000.

The total number of degrees awarded in 1950 was

445,000

.

The total number of degrees awarded in 2000 was

1,186,000

.

Consider the scatterplot to the right.

a. State whether the diagram shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, is it strong or weak?

b. Summarize any conclusions that can be drawn from the diagram.

Charitable Giving (11 States) as Percentage of Adjusted Gross Income (AGI)

\$0\$50,000\$100,00000.511.522.533.54Average AGIPercent of AGI

A scatterplot with a horizontal axis labeled Average A G I from 0 to 100000 in increments of 20000 and a vertical axis labeled Percent of A G I from 0 to 4 in increments of 0.5 contains 11 points. The coordinates of the points are as follows: (41000, 1.25); (43000, 3); (45000, 2.5); (45000, 2); (48000, 1.5); (51000, 3); (59000, 1.25); (62000, 2.25); (70000, 2.5); (80000, 3.5); (82000, 1.75). All coordinates are approximate.

a. Select the correct answer below.

A.

There is a strong positive correlation.

B.

There is a strong negative correlation.

C.

There is a weak negative correlation.

D.

There is a weak positive correlation.

E.

There is no correlation.

b. Select the correct answer below.

A.

Higher AGI may imply slightly higher charitable giving as a percentage of AGI.

B.

Higher AGI implies much higher charitable giving as a percentage of AGI.

C.

Higher AGI may imply slightly lower charitable giving as a percentage of AGI.

D.

No conclusion can be drawn.

For the following pair of variables, state the units that might be used to measure each variable. Then state whether you believe that they are correlated. If you believe they are correlated, state whether the correlation is positive or negative. Explain your reasoning.

Altitude of aircraft and air pressure

To measure altitude

,

the unit

feet above sea level

might be used.

To measure air pressure

,

the unit

pounds per square inch

might be used.

What correlation, if any, is there between the variables?

A.

There is a positive

correlation because air pressure

tends

to increase when altitude

increases

B.

There is a negative

correlation because air pressure

tends

to increase when altitude

decreases

.

C.

The variables are not correlated.

For the following pair of variables, state the units that might be used to measure each variable. Then state whether you believe that the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative. Explain your reasoning.

Altitude on a mountain hike and air pressure

To measure altitude

,

the unit

feet above sea level

might be used.

To measure air pressure

,

the unit

pounds per square inch

might be used.

What correlation, if any, is there between the variables?

A.

There is a negative

correlation because air pressure

tends

to increase when altitude

increases

.

B.

There is a positive correlation because air pressure tends to increase when altitude

decreases

.

C.

There is a positive

correlation because air pressure

tends

to increase when altitude

increases

.

D.

There is a negative

correlation because air pressure

tends

to increase when altitude

decreases

.

.

E.

The variables are not correlated.

The table to the right gives the per capita gross national product and the per capita expenditure on defense for eight developed countries. Gross domestic product (GDP) is a measure of the total economic output of a country in monetary terms. Per capita GDP is the GDP averaged over every person in the country. Complete parts a though c.

Country

Per Capita GDP (\$)

Per Capita Defense (\$)

A

36 comma 686

941

B

33 comma 153

824

C

34 comma 214

502

D

35 comma 430

1344

E

33 comma 929

329

F

47 comma 208

1225

G

35 comma 473

1006

H

45 comma 655

1729

a. Make a scatter diagram for the data.

A.

200005500002000GDPDefense Spending

A scatterplot with a horizontal axis labeled G D P from 20000 to 55000 in increments of 5000 and a vertical axis labeled Defense Spending from 0 to 2000 in increments of 200 contains 8 points. (37500, 900); (32500, 800); (35000, 500); (35000, 1300); (35000, 300); (47500, 1200); (35000, 1000); (45000, 1700). All coordinates are approximate.

.

B.

200005500002000GDPDefense Spending

A scatterplot with a horizontal axis labeled G D P from 20000 to 55000 in increments of 5000 and a vertical axis labeled Defense Spending from 0 to 2000 in increments of 200 contains 8 points. (32500, 800); (32500, 650); (35000, 600); (35000, 1450); (35000, 100); (35000, 1400); (35000, 1000); (35000, 1700). All coordinates are approximate.

C.

200005500002000GDPDefense Spending

A scatterplot with a horizontal axis labeled G D P from 20000 to 55000 in increments of 5000 and a vertical axis labeled Defense Spending from 0 to 2000 in increments of 200 contains 8 points. (37500, 1100); (32500, 1200); (35000, 1500); (35000, 700); (35000, 1700); (47500, 800); (35000, 1000); (45000, 300). All coordinates are approximate.

D.

200005500002000GDPDefense Spending

A scatterplot with a horizontal axis labeled G D P from 20000 to 55000 in increments of 5000 and a vertical axis labeled Defense Spending from 0 to 2000 in increments of 200 contains 8 points. (37500, 1700); (32500, 500); (35000, 1000); (35000, 800); (35000, 900); (47500, 300); (35000, 1300); (45000, 1300). All coordinates are approximate.

b. State whether the two variables appear to be correlated, and if so, state whether the correlation is positive, negative, strong, or weak.

A.

The two variables appear to be correlated and the correlation is strong and positive.

.

B.

The two variables appear to be correlated and the correlation is strong and negative.

C.

The two variables appear to be correlated and the correlation is weak and negative.

D.

The two variables appear to be correlated and the correlation is weak and positive.

E.

The two variables do not appear to be correlated.

c. Suggest a reason for the correlation or lack of correlation.

A.

The higher a country's per capita GDP, the more it can spend on per capita national defense.

B.

The higher a country's per capita GDP, the less it can spend on per capita national defense.

C.

There is no correlation between a country's per capita GDP and spending on per capita national defense.

MTH 216 Week 2 Checkpoint

Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.

The distribution of grades was left-skewed, but the mean, median, and mode were all the same.

A.

This does not make sense because the mean and median should lie somewhere to the left of the mode if the distribution is left-skewed.

B.

This makes sense because when outliers have high values, the mean, median, and mode are the same.

C.

This does not make sense because the mean and median should lie somewhere to the right of the mode if the distribution is left-skewed.

D.

This makes sense because when outliers have low values, the mean, median, and mode are the same.

The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the mean, median, and mode of the listed numbers.

70

49

44

77

68

60

38

30

54

35

What is the mean? Select the correct choice below and, if necessary, fill in the answer box within your choice.

A.

The mean is 52.5

.

(Round to one decimal place as needed.)

B.

There is no mean.

What is the median? Select the correct choice below and, if necessary, fill in the answer box within your choice.

A.

The median is 51.5

.

(Round to one decimal place as needed.)

B.

There is no median.

What is(are) the mode(s)? Select the correct choice below and, if necessary, fill in the answer box within your choice.

A.

The mode(s) is(are) nothing

.

(Round to one decimal place as needed. Use a comma to separate answers as needed.)

B.

There is no mode.

Blood alcohol concentrations of drivers involved in fatal crashes and then given jail sentences are shown below. Find the mean, median, and mode of the listed numbers.

0.26

0.17

0.17

0.16

0.13

0.24

0.30

0.24

0.14

0.16

0.10

0.16

The mean is 0.186

.

(Round to the nearest thousandth as needed.)

The median is 0.165

.

(Round to the nearest thousandth as needed.)

What is(are) the mode(s)? Select the correct choice below and, if necessary, fill in the answer box within your choice.

A.

The mode(s) is(are) 0.16

sec. (Use a comma to separate answers as needed.)

B.

There is no mode.

State, with an explanation, whether the mean, median, or mode gives the best description of the following average.

The average household income in this country

Which measurement gives the best description of the given average?

State, with an explanation, whether the mean, median, or mode gives the best description of the following average.

The average number of houses owned by people during their lifetime

Which measurement gives the best description of the given average?

Consider the distribution of exam scores (graded from 0 to 100) for 76

students when 38

students got an A, 22

students got a B, and 16

students got a C. Complete parts (a) through (d) below.

a. How many peaks would you expect for the distribution?

A.

There would probably be three peaks, because even though each exam score could be anywhere between 0 and 100, the only grades received were A, B, and C.

B.

There would probably be one peak because there are no obvious reasons why the exam scores would form different groups.

C.

There would probably be no peaks. The distribution of grades always tends to be uniform.

D.

There would probably be many peaks corresponding to the different exam scores that each student had.

b. Make a sketch of the distribution. Choose the correct answer below.

c. What shape would you expect for the distribution?

A.

The distribution would probably be symmetric because there are no obvious factors to indicate that there would be a higher or lower exam score for any student.

B.

The distribution would probably be symmetric because the only grades received were A, B, and C.

C.

The distribution would probably be left-skewed because many of the students got an A, and very few got a C.

D.

The distribution would probably be right-skewed because a lot of students got either a B or a C.

d. What variation would you expect in the distribution?

A.

The variation would probably be large because many students got an A, some got a B, and a small number got a C.

B.

The variation would probably be moderate because the only grades received were A, B, and C.

C.

The variation would probably be moderate because there are no obvious reasons to expect an especially large or small amount of variation.

D.

The variation would probably be small because all the students would tend to have nearly the same exam score.

Suppose you study family income in a random sample of 200

families. Your results can be summarized as the mean family income was \$46 comma 000

,

the median family income was \$ 30 comma 000

,

the highest and lowest incomes were \$254 comma 000

and \$2 comma 200

,

respectively.

a. Draw a rough sketch of the income distribution, with clearly labeled axes. Choose the correct answer below.

Describe the distribution as symmetric, left-skewed, or right-skewed. Choose the correct answer below.

right-skewed

symmetric

left-skewed

b. How many families in the sample earned less than \$30 comma 000

?

Explain how you know. Choose the correct answer below.

A.

150

families, because the mode is the most common value in a data set.

B.

50

families, because the mean is the average value of income.

C.

100

families, because the median is the middle value in the sorted data set.

c. Based on the given data, can you determine how many families earned more than \$ 46 comma 000

?

Why or why not? Choose the correct answer below.

A.

No, because the number of families that earned more than \$ 46 comma 000

depends on the distribution.

B.

Yes, because the mean is the middle value in the sorted data set.

The table to the right gives the cost of living index (COLI) for six East Coast counties and six Midwest counties (using an index where 100 represents the average cost of living for all participating cities with a population of more than 1.5 million). Answer parts (a) through (e) below.

a. Find the mean, median, and range for each of the two data sets.

The mean for the East Coast Counties is 157.68

.

(Type an integer or decimal rounded to two decimal places as needed.)

The median for the East Coast Counties is 131.4

.

(Type an integer or decimal rounded to two decimal places as needed.)

The range for the East Coast Counties is 210.8

.

(Type an integer or decimal rounded to two decimal places as needed.)

The mean for the Midwest Counties is 115.83

.

(Type an integer or decimal rounded to two decimal places as needed.)

The median for the Midwest Counties is 95.4

.

(Type an integer or decimal rounded to two decimal places as needed.)

The range for the Midwest Counties is 141.3

.

(Type an integer or decimal rounded to two decimal places as needed.)

b. Give the five-number summary and draw a boxplot for each of the two data sets.

Give the five number summary for the East Coast Counties.

Low Value

equals

104.1

Lower Quartile

equals

123.10

Median

equals

131.4

Upper Quartile

equals

141.2

High Value

equals

314.9

(Type integers or decimals rounded to two decimal places as needed.)

Give the five-number summary for the Midwest Counties.

Low Value

equals

87.2

Lower Quartile

equals

92.2

Median

equals

95.4

Upper Quartile

equals

96.3

High Value

equals

228.5

(Type integers or decimals rounded to two decimal places as needed.)

Choose the correct boxplot for the Midwest Counties below.

A.

80120160200240x

A boxplot is above a number line that is labeled from 80 to 240 in increments of 20. A box extends from 123 to 141. A horizontal line segment extends from the left side of the box and intersects a short vertical line segment at 104. A horizontal line segment extends from the right side of the box to 240. All values are approximate.

B.

80120160200240x

A boxplot is above a number line that is labeled from 80 to 240 in increments of 20. A box extends from 111 to 113. A horizontal line segment extends from the left side of the box and intersects short vertical line segments at 105 and 87. A horizontal line segment extends from the right side of the box and intersects a short vertical line segment at 229. All values are approximate.

C.

80120160200240x

A boxplot is above a number line that is labeled from 80 to 240 in increments of 20. A box extends from 92 to 96, with a vertical line segment through the box at 95. A horizontal line segment extends from the left side of the box and intersects a short vertical line segment at 87. A horizontal line segment extends from the right side of the box and intersects a short vertical line segment at 229. All values are approximate.

c. Find the standard deviation for each of the two data sets.

The standard deviation for the East Coast Counties is 78.05

.

(Type an integer or decimal rounded to two decimal places as needed.)

The standard deviation for the Midwest Counties is 55.30

.

(Type an integer or decimal rounded to two decimal places as needed.)

d. Apply the range rule of thumb to estimate the standard deviation of each of the two data sets. How well does the rule work in each case? Briefly discuss why it does or does not work well.

The standard deviation for the East Coast Counties is approximately 52.7

,

using the range rule of thumb.

(Type an integer or decimal rounded to two decimal places as needed.)

The standard deviation for the Midwest Counties is approximately 35.33

,

using the range rule of thumb.

(Type an integer or decimal rounded to two decimal places as needed.)

How well does the rule work in each case? Briefly discuss why it does or does not work well. Choose the correct answer below.

A.

They work well in both of the two data sets because there are no outliers in anyone of the two data sets.

B.

It works well in the Midwest data set, but it does not work well in the East Coast data set, because there is a outlier in the East Coast data set.

C.

They do not work well in both of the two data sets because there are outliers in both of the two data sets.

D.

It works well in the East Coast data set, but it does not work well in the Midwest data set, because there is a outlier in the Midwest data set.

e. Based on all the results, compare and discuss the two data sets in terms of their center and variation. Choose the correct answer below. Select all that apply.

A.

The variation of COLI for the six East Coast counties is higher than that for the six Midwest Counties, which means the level of COLI in most Midwest Counties varies in a larger range.

B.

The mean of COLI for the six East Coast counties is higher than that for the six Midwest Counties, which means the average level of COLI for the East Coast counties is higher.

C.

The variation of COLI for the six East Coast counties is higher than that for the six Midwest Counties, which means the level of COLI in most Midwest Counties varies in a smaller range.

D.

The mean of COLI for the six East Coast counties is higher than that for the six Midwest Counties, which means the average level of COLI for the East Coast counties is lower.

Decide whether the following statement makes sense or does not make sense.

The heights of male basketball players at a local college are normally distributed with a mean of 6 feet 3 inches and a standard deviation of 3 inches.

Does not make sense

Makes sense

Decide whether the following statement makes sense or does not make sense.

The weights of babies born at Belmont Hospital are normally distributed with a mean of 6.8 pounds and a standard deviation of 7 pounds.

Does not make sense

Makes sense

MTH 216 Week 3 Checkpoint

Fill in the remaining entries in the two-way table shown to the right.

A survey of 140

patrons at a restaurant gave the preferences for entrees and drinks shown to the right

Decide whether the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.

I made a frequency table with two columns, one labeled "State" and one labeled "State Capitol."

A.

The statement makes sense. In a frequency table, each category listed in one column has a characteristic about it in the second column. The table described in the given statement has this property.

B.

The statement does not make sense. In a frequency table, each category must have a frequency greater than 1. Because each state has exactly one capitol, each category in the table described in the given statement would have frequency 1.

C.

The statement does not make sense. In a frequency table, one of the columns lists the frequency of each category, which is the number of data values in the category. The table described in the given statement does not have this column.

D.

The statement makes sense. The set of states is clearly defined and each state has a clearly defined capitol.

Decide whether the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.

Your pie chart must be wrong, because you have the 45% frequency wedge near the upper left and the answer key shows it near the lower right.

A.

The statement does not make sense. Although the student's pie chart may be wrong for another reason, it does not matter where in a pie chart a wedge is located so long as it is labeled clearly.

B.

The statement does not make sense. The person's pie chart is merely the mirror image of the pie chart in the answer key, so it is still correct.

C.

The statement makes sense. In a pie chart, the largest wedge should always be in the lower right.

D.

The statement makes sense. Pie charts show frequencies, which are whole numbers, and not relative frequencies, which are fractions or percentages.

Determine whether the data described are qualitative or quantitative.

The weights of subjects in a clinical trial of a new drug

qualitative

quantitative

Determine whether the following variable is qualitative or quantitative.

The yes/no responses on a ballot initiative to the question "Should cigarette taxes be

increased question mark "

nothing

A.

The variable is qualitative because yes/no responses on a ballot initiative are nonnumerical categories.

B.

The variable is quantitative because the yes and no responses can be counted to determine the outcome of the initiative.

C.

The variable is quantitative because it is possible to count the number of responses and check that each voter gave only one.

D.

The variable is qualitative because a voter's response on a ballot initiative depends on his or her opinions.

Use the frequency table for the ages of recent award-winning male actors at the time when they won their award to construct the corresponding histogram.

Click the icon to view the frequency table.

If X is correlated with Y, what must be true about X and Y? Explain your reasoning.

A.

Increasing values of X go with either increasing or decreasing values of Y. A correlation exists between X and Y when higher values of X consistently go with higher values of Y or when higher values of X consistently go with lower values of Y.

B.

Increasing values of X go with increasing values of Y. A correlation exists between two variables when both variables decrease together.

C.

Increasing values of X go with either increasing or decreasing values of Y. A correlation exists between two variables when both variables increase or decrease together.

D.

X causes Y. If Y increases as X increases, then X must cause Y to change.

E.

Increasing values of X go with increasing values of Y. A correlation exists between two variables when both variables increase together.

F.

X causes Y. If Y decreases as X increases, then X must cause Y to change.

If the points on a scatterplot fall on a nearly straight line sloping upward, what do the two variables have? Explain your reasoning.

A.

A weak negative correlation. A negative correlation is when both variables increase or decrease together, and a weak correlation is when the two variables lie close to a straight line.

B.

No correlation. The given information does not indicate a relationship between the two variables.

C.

A weak negative correlation. A negative correlation is when both variables increase together, and a weak correlation is when the two variables lie exactly on a straight line.

D.

No correlation. There is only a correlation between two variables when one variable decreases while the other increases.

E.

A strong positive correlation. A positive correlation is when both variables increase together, and a strong correlation is when the two variables lie exactly on a straight line.

F.

A strong positive correlation. A positive correlation is when both variables increase or decrease together, and a strong correlation is when the two variables lie close to a straight line.

You have found a higher rate of birth defects among babies born to women exposed to second-hand smoke. To support a claim that the second-hand smoke caused the birth defects, what else should you expect to find? Explain your reasoning.

A.

Evidence that these types of birth defects occur only in babies whose mothers were exposed to smoke and never to any other babies. If the birth defects are caused by second-hand smoke, then the birth defects should not be present in babies whose mothers were not exposed to second-hand smoke.

B.

Evidence that the types of birth defects in these babies are more debilitating than other types of birth defects. Second-hand smoke causes the worst kind of birth defects.

C.

Evidence that higher rates of defects are correlated with exposure to greater amounts of smoke. If higher rates of defects are correlated with exposure to greater amounts of smoke, it is more likely that the second-hand smoke is a cause of the birth defects.

D.

Evidence that these types of birth defects occur only in babies whose mothers were exposed to smoke and never to any other babies. If second-hand smoke is the cause of the birth defects, there can be no other causes.

E.

Evidence that higher rates of defects are correlated with exposure to greater amounts of smoke. If higher rates of defects are correlated with exposure to greater amounts of smoke, it is less likely that the second-hand smoke is a cause of the birth defects.

Which of the following best describes the correlation between accidents and texting while driving? Explain your reasoning.

A.

There is a common underlying cause because many of the same people who text while driving are distracted by other things on the road.

B.

There is a common underlying cause because many people make plans through texting and drive to get where they are going.

C.

It is a coincidence because texting while driving and accidents are not related.

D.

It is a coincidence because texting while driving has no effect on the driver's ability to pay attention to the road.

E.

Texting while driving is a likely cause of accidents because texting is necessary and takes precedence over driving.

F.

Texting while driving is a likely cause of accidents because texting is a distraction from driving.

MTH 216 Week 4 Checkpoint

A restaurant offers 9

appetizers and 10

main courses.  In how many ways can a person order a two-course meal?  Use the multiplication principle with two groups of items.

There are 90

ways a person can order a two-course meal.

Pizza House offers 4

different kinds of pizza, and 6

different desserts. How many different three course meals can be ordered?

Find the odds for and the odds against the event rolling a fair die and getting a 4 comma a 3 comma a 5 comma or a 2.

a. The odds for the event are 2

to 1

.

b. The odds against the event are 1

to 2

.

The odds on (against) your bet are 7

to 6

.

If you bet \$48

and win, how much will you gain?

Suppose you toss a fair coin 10,000 times. Should you expect to get exactly 5000 heads? Why or why not? What does the law of large numbers tell you about the results you are likely to get?

Should you expect to get exactly 5000 heads? Why or why not? Choose the correct answer below.

A.

You shouldn't expect to get exactly 5000 heads, because you cannot predict precisely how many heads will occur.

B.

You should expect to get exactly 5000 heads, because for a fair coin, the proportion of heads is exactly 50%.

C.

You shouldn't expect to get exactly 5000 heads, because it is not easy to count precisely the number of heads that occurred.

D.

You should expect to get exactly 5000 heads, because the proportion of heads should be 50% for such a large number of tosses.

What does the law of large numbers tell you about the results you are likely to get?

A.

The proportion of heads should not approach 0.5 as the number of tosses increases.

B.

The proportion of heads should approach 0.5 as the number of tosses increases.

C.

The proportion of heads should approach 0.5 as the number of tosses decreases.

D.

The proportion of heads should approach 0.5 as the number of tosses approaches an exact number.

The table shows the leading causes of death in a certain country in a recent year. The population of the country was 313

million. What is the empirical probability of death by pneumonia or influenza

during a single year? How much greater is the risk of death by pneumonia or influenza

than death by kidney disease

Use the graph to estimate the death rate for 65

-year-olds.

Assuming that there were about 11.6

million 65

-year-olds,

how many people of this age could be expected to die in a year?

The estimated death rate for 65

-year-olds

is 20

deaths per 1000 people.

(Round to the nearest whole number as needed.)

Assuming that there were about 11.6 million

65

-year-olds,

232000

people of this age could be expected to die in a year.

In a certain country, the life expectancy for women in 1900 was 47

years and in 2000 it was 75

years. Assuming that life expectancy between 2000 and 2100 increases by the same percentage as it did between 1900 and 2000, what will the life expectancy be for women in 2100?

Assuming the life expectancy between 2000 and 2100 will increase by the same percentage as it did between 1900 and 2000, the life expectancy for women in 2100 will be 120

years.

Baby Brianna

wants to arrange 5

blocks in a row. How many different arrangements can she

make?

There are 120

ways to arrange the 5

blocks.

Answer the following question using the appropriate counting technique, which may be either arrangements with repetition, permutations, or combinations. Be sure to explain why this counting technique applies to the problem.

How many possible birth orders with respect to gender are possible in a family with seven

children? (For example, BBGGBBB and BGBBBBG

are different orders.)

What counting technique should be used to make this calculation?

A.

Arrangements with repetitions because the selections come from a single group of items,  and the order of the arrangement matters.

B.

Combinations because the selections come from a single group of items, no item can be selected more than once and the order of the arrangement does not matter.

C.

Permutations because the selections come from a single group of items, no item can be selected more than once and the order of the arrangement matters.

D.

Arrangements with repetitions because there are r selections from a group of n choices and choices can be repeated.

There are 128

possible birth orders for a family with seven

children.

Find the probability of the given event.

Choosing eight

numbers that match eight

randomly selected balls when the balls are numbered 1 through 32

.

The probability of the given event is StartFraction 1 Over 10518300 EndFraction

.

MTH 216 Week 5 Checkpoint

Compute the total cost per year of the following pair of expenses. Then complete the sentence: On an annual basis, the first set of expenses is _______% of the second set of expenses.

Maria spends \$15

on lottery tickets every week and spends \$139

per month on food.

On an annual basis, the money spent on lottery tickets is 47

%

of the money spent to buy food.

Consider a relatively simple health insurance plan with the following provisions. Office visits require a co-payment of \$25

.

Emergency room visits have a \$250

co-payment. Surgical operations have a \$1 comma 700

deductible (the first \$1 comma 700

is paid out of pocket). The monthly premium is \$360

.

During a one-year period, somebody insured by this health insurance has the expenses shown to the right. Complete parts (a) and (b) below.

Expenses

Total Cost

Feb. 18: Office visit

\$150

Mar. 26:Emergency room

\$720

Apr. 23: Office visit

\$150

May 14: Surgery

\$6 comma 500

July 1: Office visit

\$150

Sept. 23: Emergency room

\$950

a. Determine the person's health care expenses for the year with the insurance policy.

The person's health care expenses with the insurance policy are \$6595

.

(Type a whole number.)

b. Determine the person's health care expenses for the year without the insurance policy.

The person's health care expenses without the insurance policy are \$8620

.

Calculate the amount of money you'll have at the end of the indicated time period.

You invest \$1000

in an account that pays simple interest of 7

%

for 20

years.

The amount of money you'll have at the end of 20

years is \$2400

.

Find the annual percentage yield (APY) in the following situation.

A bank offers an APR of 6.6

%

compounded daily.

The annual percentage yield is 6.82

%.

Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account.

A \$17 comma 000

deposit in an account with an APR of 4.75

%.

The balance in the account after 1

year is approximately \$17826.99

.

(Round to the nearest cent as needed.)

The balance in the account after 5

years is approximately \$21557.27

.

(Round to the nearest cent as needed.)

The balance in the account after 20

years is approximately \$43957.06

.

(Round to the nearest cent as needed.)

The APY for the account is approximately 4.86

%

Use the savings plan formula to answer the following question.

Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 6 %

.

How much should you deposit monthly to accumulate \$83 comma 000

in 13

years?

You should invest \$352.52

each month.

Compute the total and annual returns on the described investment.

Six

shares of XYZ stock for \$40

per share, you sell the stock for \$ 2900.

The total return is 45

%.

(Do not round until the final answer. Then round to one decimal place as needed.)

The annual return is 6.4

%.

(Do not round until the final answer. Then round to one decimal place as needed.)

Consider a home mortgage of \$200 comma 000

at a fixed APR of 6

%

for 20

years.

a. Calculate the monthly payment.

b. Determine the total amount paid over the term of the loan.

c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

a. The monthly payment is \$1432.86

.

(Do not round until the final answer. Then round to the nearest cent as needed.)

b. The total amount paid over the term of the loan is \$343886.4

.

(Round to the nearest cent as needed.)

c. Of the total amount paid, 58.2

%

is paid toward the principal, and 41.8

%

is paid for interest.

(Round to one decimal place as needed.)

Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs.

You need a \$140 comma 000

loan.

Option 1: a 30-year loan at an APR of 7

%.

Option 2: a 15-year loan at an APR of 6.5

%.

Find the monthly payment for each option.

The monthly payment for option 1 is \$931.42

.

The monthly payment for option 2 is \$1219.55

.

(Do not round until the final answer. Then round to the nearest cent as needed.)

Find the total amount paid for each option.

The total payment for option 1 is \$335311.2

.

The total payment for option 2 is \$219519

.

(Use the answers from the previous step to find this answer. Round to the nearest cent as needed.)

Compare the two options. Which appears to be the better option?

A.

Option 2 is the better option, but only if the borrower can afford the higher monthly payments over the entire term of the loan.

B.

Option 2 will always be the better option

C.

Option 1 will always be the better option.

D.

Option 1 is the better option, but only if the borrower plans to stay in the same home for the entire term of the loan.

A man

earned wages of \$41 comma 700

,

in interest from a savings account, and contributed \$3400

to a tax-deferred retirement plan. He

was entitled to a personal exemption of \$2700

.

Find his

gross income, adjusted gross income, and taxable income.

His

gross income was \$43400

.

His

.

His

taxable income was \$31830

.

Use the marginal tax rates in the table below to compute the tax owed in the following situation.

Marco

is married filing separately

with

a taxable income of \$67 comma 600

.

Tax Rate

Single

Married Filing Separately

10%

up to \$8,925

up to \$8,925

15%

up to \$36,250

up to \$36,250

25%

up to \$87,850

up to \$73,200

28%

up to \$183,250

up to \$111,525

33%

up to \$398,350

up to \$199,175

35%

up to \$400,000

up to \$400,000

standard deduction

\$6100

\$6100

exemption (per person)

\$3900

\$3900

The tax owed is \$12829

.

You are in the 25 %

tax bracket. The apartment rents for \$ 1500

per month. Your monthly mortgage payments would be \$2200

,

of which an average of \$1900

per month goes toward interest during the first year. Determine whether renting or buying is cheaper in terms of monthly payments during the first year. Assume you are itemizing deductions.

Is it cheaper to own or to rent?

It is cheaper to rent

.

It is cheaper to own

.