find the regression equation for predicting final

The accompanying scatterplots concern the total assessed value of properties that include? homes, and both depict the same observations. Complete parts? (a) and? (b) below.

LOADING...

Click the icon to view the scatterplots.

a. Which do you think has a stronger relationship with value of the 

propertylong dash

the 

number of square feet in the home or the number of fireplaces in the? home? Why?

A.

The number of square feet has a stronger relationship with the value of the? property, as shown by the fact that the points are more scattered in a vertical direction.

B.

The number of square feet has a stronger relationship with the value of the? property, as shown by the fact that the points are less scattered in a vertical direction.

This is the correct answer.

C.

The number of fireplaces has a stronger relationship with the value of the? property, as shown by the fact that the points are less scattered in a vertical direction.

D.

The number of fireplaces has a stronger relationship with the value of the? property, as shown by the fact that the points are more scattered in a vertical direction.

b. If you were trying to predict the value of a property? (where there is a? home) in this? area, would you be able to make a better prediction by knowing the number of square feet or the number of? fireplaces? Explain. Choose the correct answer below.

A.

Square feet. Total value is more strongly associated with square? feet, because there is less variability in total value for any given value of square feet.

This is the correct answer.

B.

Fireplaces. Total value is more strongly associated with? fireplace, because there is less variability in total value for any given value of number of fireplaces.

C.

Neither because the association is the same between the value of property and square feet and the value of property and the number of fireplaces.

  

The scatterplot shows the number   of work hours and the number of TV hours per week for some college students   who work. There is a very slight trend. Is the trend positive or? negative?   What does the direction of the trend mean in this? context? Identify any   unusual points.

 

A scatterplot has a horizontal   axis labeled "Work Hours" from 10 to 70 in intervals of 10 and a   vertical axis labeled "TV Hours" from 0 to 30 in intervals of 5.   Points plotted have a somewhat negative trend between approximately (10, 30)   and (5, 50), with average vertical spread around 15. all points remain within   the horizontal bounds between 10 and 50, with the exception of one point at   70. 

What is the? trend? What does the direction of the trend? mean? Choose the correct answer below.

A.

The trend is negative. The more hours of work a student? has, the more hours of TV the student tends to watch.

B.

The trend is positive. The more hours of work a student? has, the fewer hours of TV the student tends to watch.

C.

The trend is negative. The more hours of work a student? has, the fewer hours of TV the student tends to watch.

This is the correct answer.

D.

The trend is positive. The more hours of work a student? has, the more hours of TV the student tends to watch.

Identify any unusual points. Select the correct choice below? and, if? necessary, fill in the answer box to complete your choice.

A.

The person who works 

70

hours appears to be an? outlier, because that point is separated from the other points by a large amount.

B.

The person who works 

nothing

hours is an unusual? point, because there? aren't that many hours in a week.

C.

There are no unusual points in this graph

  

The table to the right shows the   number of people living in a house and the weight of trash? (in pounds) at   the curb just before trash pickup. Complete parts? (a) through? (c) below.

People

Trash?   (pounds)

3

24    

3

28    

5   

76    

2

16     

7

83

 a. Find the correlation between these numbers by using a computer or a statistical calculator.

requals

0.956

?(Round to three decimal places as? needed.)

b. Suppose some of the weight was from the container? (each container weighs 

5

?pounds). Subtract 

5

pounds from each? weight, and find the new correlation with the number of people. What happens to the correlation when a constant is added? (we added negative 

5

?) 

to each? number?

?(Round to three decimal places as? needed.)

A.

The correlation is 

nothing

The correlation coefficient decreases when a constant is added to each number.

B.

The correlation is 

0.956

. 

The correlation coefficient remains the same when a constant is added to each number.

C.

The correlation is 

nothing

. 

The correlation coefficient increases when a constant is added to each number.

c. Suppose each house contained exactly 

four times

the number of? people, but the weight of the trash was the same. What happens to the correlation when numbers are multiplied by a? constant?

?(Round to three decimal places as? needed.)

A.

The correlation is 

nothing

The correlation coefficient increases when the numbers are multiplied by a positive constant.

B.

The correlation is 

0.956

. 

The correlation coefficient remains the same when the numbers are multiplied by a positive constant.

C.

The correlation is 

nothing

. 

The correlation coefficient decreases when the numbers are multiplied by a positive constant.

he accompanying computer output is for predicting foot length from hand length? (in cm) for a group of women. Assume the trend is linear. Summary statistics for the data are shown in the accompanying table. Complete parts? (a) through? (d) below.

LOADING...

Click the icon to see the computer output and summary statistics.

a. Report the regression? equation, using the words? "Hand" and? "Foot," not x and y.

  

Predicted   Foot 

equals

15.910

plus0.578

  

Hand 

  

?(Round to three decimal places   as? needed.)

b. Verify the slope by using the formula 

bequals

r StartFraction s Subscript y Over s Subscript x EndFraction

. 

Substitute the values into the formula.

  

b

 

equals

r StartFraction s Subscript y Over s Subscript x EndFraction

   

equals

left parenthesis nothing right parenthesis times StartFraction left parenthesis nothing right parenthesis Over left parenthesis nothing right parenthesis EndFraction

       

?(Type integers or decimals. Do     not? round.)

Simplify the right side of the   equation to verify the slope.

  

b

 

equals

0.578

       

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

c. Verify the? y-intercept by   using the formula 

aequals

y overbar minus b x overbar

. 

Substitute the values into the formula.

  

a

 

equals

y overbar minus b x overbar

   

equals

left parenthesis nothing right parenthesis minus left parenthesis nothing right parenthesis left parenthesis nothing right parenthesis

       

?(Round to three decimal places     as needed. Type the terms of your expression in the same order as they     appear in the original? expression.)

Simplify the right side of the   equation to verify the? y-intercept.

  

a

 

equals

15.91

    

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

 

incorrect, 4.3.50 

              

The accompanying table shows the? self-reported number of semesters completed and the number of units completed for 15 students at a community college. All units were? counted, but attending summer school was not included. Complete parts? (a) through? (e) below.

LOADING...

Click the icon to view the data table.

a. Make a scatterplot with the number of semesters on the? x-axis and the number of units on the? y-axis. Choose the correct scatterplot below.

A.

0100150SemestersUnits

A scatterplot with a horizontal axis labeled “Semesters” from 0 to 10 in intervals of 1 and a vertical axis labeled “Units” from 0 to 150 in intervals of 25 contains the following 15 plotted points: (1, 10); (3, 40); (3, 85); (4, 80); (5, 85); (6, 95); (6, 100); (6, 110); (7, 5); (7, 120); (7, 120); (7, 125); (8, 105); (8, 120); (10, 150). The points have the pattern of a straight line that rises from left to right between points (0, 25) and (10, 140), with average vertical spread of about 25. The points have an average vertical spread of about 25, except for the outlier at (7, 5). All coordinates are approximate.

B.

0100150SemestersUnits

A scatterplot with a horizontal axis labeled “Semesters” from 0 to 10 in intervals of 1 and a vertical axis labeled “Units” from 0 to 150 in intervals of 25 contains the following 15 plotted points: (0, 150); (2, 105); (2, 120); (3, 5); (3, 120); (3, 120); (3, 125); (4, 95); (4, 100); (4, 110); (5, 85); (6, 80); (7, 40); (7, 85); (9, 10). The points have the pattern of a straight line that falls from left to right between points (0, 140) and (10, 25), with average vertical spread of about 25. The points have an average vertical spread of about 25, except for the outlier at (3, 5). All coordinates are approximate.

C.

0100150SemestersUnits

A scatterplot with a horizontal axis labeled “Semesters” from 0 to 10 in intervals of 1 and a vertical axis labeled “Units” from 0 to 150 in intervals of 25 contains the following 15 plotted points: (1, 140); (3, 65); (3, 110); (4, 70); (5, 65); (6, 40); (6, 50); (6, 55); (7, 25); (7, 30); (7, 30); (7, 145); (8, 30); (8, 45); (10, 0). The points have the pattern of a straight line that falls from left to right between points (0, 125) and (10, 10), with average vertical spread of about 25. The points have an average vertical spread of about 25, except for the outlier at (7, 145). All coordinates are approximate.

D.

0100150SemestersUnits

A scatterplot with a horizontal axis labeled “Semesters” from 0 to 10 in intervals of 1 and a vertical axis labeled “Units” from 0 to 150 in intervals of 25 contains the following 15 plotted points: (0, 0); (2, 30); (2, 45); (3, 25); (3, 30); (3, 30); (3, 145); (4, 40); (4, 50); (4, 55); (5, 65); (6, 70); (7, 65); (7, 110); (9, 140). The points have the pattern of a straight line that rises from left to right between points (0, 10) and (10, 125), with average vertical spread of about 25. The points have an average vertical spread of about 25, except for the outlier at (3, 145). All coordinates are approximate.

This is the correct answer.

Does one point stand out as? unusual? Explain why it is unusual.

A.

The point 

?(3

?,145.0

?) 

stands out as unusual because its? y-value is much lower than the ? y-values of other data points with similar? x-values.

B.

The point 

?(2

?,44.5

?) 

stands out as unusual because it is not possible for a person to complete a fraction of a unit.

C.

The point 

?(3

?,145.0

?) 

stands out as unusual because its? y-value is much higher than the ? y-values of other data points with similar? x-values.

This is the correct answer.

D.

The point 

?(0

?,0.0

?) 

stands out as unusual because the person has not completed any units.

b. Find the numerical value for the? correlation, including the unusual point.

The correlation is 

0.682

?(Round to three decimal places as? needed.)

Find the numerical value for the correlation when the unusual point is not included.

The correlation is 

0.927

.

?(Round to three decimal places as? needed.)

Comment on the difference in correlation when the unusual point is removed.

A.

When the unusual point is removed from the data? set, the correlation increases because the point is very close to the line.

B.

When the unusual point is removed from the data? set, the correlation decreases because the point is very close to the line.

C.

When the unusual point is removed from the data? set, the correlation decreases because the point is far from the line.

D.

When the unusual point is removed from the data? set, the correlation increases because the point is far from the line.

This is the correct answer.

c. Report the equation of the regression? line, including the unusual point.

Predicted 

Unitsequals

10.0plusleft parenthesis nothing right parenthesis

Semesters

?(Round to one decimal place as? needed.)

Report the equation of the regression line when the unusual point is not included.

Predicted 

Unitsequals

negative 3.8plusleft parenthesis nothing right parenthesis

Semesters

?(Round to one decimal place as? needed.)

Comment on the difference in the equation of the regression line when the unusual point is removed.

A.

When the unusual point is? removed, the intercept of the equation decreases and the slope increases.

This is the correct answer.

B.

When the unusual point is? removed, the intercept and the slope of the equation both decrease.

C.

When the unusual point is? removed, the intercept and the slope of the equation both increase.

D.

When the unusual point is? removed, the intercept of the equation increases and the slope decreases.

d. Insert the regression line into the scatterplot found? earlier, including the unusual point. Use technology if possible. Choose the correct graph below.

A.

0100150SemestersUnits

A scatterplot with a horizontal axis labeled “Semesters” from 0 to 10 in intervals of 1 and a vertical axis labeled “Units” from 0 to 150 in intervals of 25 contains the following 15 plotted points: (0, 0); (2, 30); (2, 45); (3, 25); (3, 30); (3, 30); (3, 145); (4, 40); (4, 50); (4, 55); (5, 65); (6, 70); (7, 65); (7, 110); (9, 140). The points have the pattern of a straight line that rises from left to right between points (0, 10) and (125, 9), with average vertical spread of about 25. The points have an average vertical spread of about 25, except for the outlier at (3, 145). On the same graph is a line which rises from left to right between points (0, 10) and (125, 9). All coordinates are approximate.

This is the correct answer.

B.

0100150SemestersUnits

A scatterplot with a horizontal axis labeled “Semesters” from 0 to 10 in intervals of 1 and a vertical axis labeled “Units” from 0 to 150 in intervals of 25 contains the following 15 plotted points: (0, 150); (2, 105); (2, 120); (3, 5); (3, 120); (3, 120); (3, 125); (4, 95); (4, 100); (4, 110); (5, 85); (6, 80); (7, 40); (7, 85); (9, 10). The points have the pattern of a straight line that falls from left to right between points (0, 140) and (10, 25), with average vertical spread of about 25. The points have an average vertical spread of about 25, except for the outlier at (3, 5). On the same graph is a line which falls from left to right between points (0, 140) and (9, 30). All coordinates are approximate.

C.

0100150SemestersUnits

A scatterplot with a horizontal axis labeled “Semesters” from 0 to 10 in intervals of 1 and a vertical axis labeled “Units” from 0 to 150 in intervals of 25 contains the following 15 plotted points: (1, 140); (3, 65); (3, 110); (4, 70); (5, 65); (6, 40); (6, 50); (6, 55); (7, 25); (7, 30); (7, 30); (7, 145); (8, 30); (8, 45); (10, 0). The points have the pattern of a straight line that falls from left to right between points (1, 120) and (10, 10), with average vertical spread of about 25. The points have an average vertical spread of about 25, except for the outlier at (7, 145). On the same graph is a line which falls from left to right between points (1, 120) and (10, 10). All coordinates are approximate.

D.

0100150SemestersUnits

A scatterplot with a horizontal axis labeled “Semesters” from 0 to 10 in intervals of 1 and a vertical axis labeled “Units” from 0 to 150 in intervals of 25 contains the following 15 plotted points: (1, 10); (3, 40); (3, 85); (4, 80); (5, 85); (6, 95); (6, 100); (6, 110); (7, 5); (7, 120); (7, 120); (7, 125); (8, 105); (8, 120); (10, 150). The points have the pattern of a straight line that rises from left to right between points (0, 25) and (10, 140), with average vertical spread of about 25. The points have an average vertical spread of about 25, except for the outlier at (7, 5). On the same graph is a line which rises from left to right between points (1, 30) and (10, 140). All coordinates are approximate.

Insert the regression line into the scatterplot found earlier when the unusual point is removed. Use technology if possible. Choose the correct graph below.

A.

0100150SemestersUnits

A scatterplot with a horizontal axis labeled “Semesters” from 0 to 10 in intervals of 1 and a vertical axis labeled “Units” from 0 to 150 in intervals of 25 contains the following 15 plotted points: (0, 150); (2, 105); (2, 120); (3, 5); (3, 120); (3, 120); (3, 125); (4, 95); (4, 100); (4, 110); (5, 85); (6, 80); (7, 40); (7, 85); (9, 10). The points have the pattern of a straight line that falls from left to right between points (0, 140) and (10, 25), with average vertical spread of about 25. On the same graph is a line which falls from left to right between points (0, 120) and (9, 55). All coordinates are approximate.

B.

0100150SemestersUnits

A scatterplot with a horizontal axis labeled “Semesters” from 0 to 10 in intervals of 1 and a vertical axis labeled “Units” from 0 to 150 in intervals of 25 contains the following 15 plotted points: (1, 140); (3, 65); (3, 110); (4, 70); (5, 65); (6, 40); (6, 50); (6, 55); (7, 25); (7, 30); (7, 30); (7, 145); (8, 30); (8, 45); (10, 0). The points have the pattern of a straight line that falls from left to right between points (1, 80) and (10, 19), with average vertical spread of about 25. On the same graph is a line which falls from left to right between points (1, 80) and (10, 19). All coordinates are approximate.

C.

0100150SemestersUnits

A scatterplot with a horizontal axis labeled “Semesters” from 0 to 10 in intervals of 1 and a vertical axis labeled “Units” from 0 to 150 in intervals of 25 contains the following 15 plotted points: (1, 10); (3, 40); (3, 85); (4, 80); (5, 85); (6, 95); (6, 100); (6, 110); (7, 5); (7, 120); (7, 120); (7, 125); (8, 105); (8, 120); (10, 150). The points have the pattern of a straight line that rises from left to right between points (0, 25) and (10, 140), with average vertical spread of about 25. On the same graph is a line which rises from left to right between points (1, 25) and (10, 155). All coordinates are approximate.

D.

0100150SemestersUnits

A scatterplot with a horizontal axis labeled “Semesters” from 0 to 10 in intervals of 1 and a vertical axis labeled “Units” from 0 to 150 in intervals of 25 contains the following 15 plotted points: (0, 0); (2, 45); (3, 25); (3, 30); (3, 30); (3, 145); (4, 40); (4, 50); (4, 55); (5, 65); (6, 70); (7, 65); (7, 110); (9, 140). The points have the pattern of a straight line that rises from left to right between points (0, 10) and (130, 9), with average vertical spread of about 25. On the same graph is a line which rises from left to right between points (0, negative 5) and (130, 9). All coordinates are approximate.

This is the correct answer.

Comment on the difference in the regression lines when the unusual point is removed.

A.

When the unusual point is removed from the? data, the regression line seems to be a worse fit for the points on the scatterplot.

B.

When the unusual point is removed from the? data, the regression line seems to be a better fit for the points on the scatterplot.

This is the correct answer.

C.

When the unusual point is removed from the? data, the slope of the regression line changes from positive to negative.

D.

When the unusual point is removed from the? data, the slope of the regression line changes from negative to positive.

e. Report the slope and intercept of the regression line when the unusual point is included and explain what it shows. If the intercept is not appropriate to? report, explain why. Select the correct choice below and fill in the answer boxes to complete your choice.

?(Round to one decimal place as? needed.)

A.

The slope shows? that, for each additional unit? completed, the average number of semesters completed will increase by 

nothing

. 

The intercept shows that when the average student has completed zero units they will have completed 

nothing

semesters.

B.

The slope shows? that, for each additional semester? completed, the average number of units completed will increase by 

nothing

. 

It is not appropriate to report the intercept because a student cannot complete 

nothing

units.

C.

The slope shows? that, for each additional semester? completed, the average number of units completed will increase by 

12.2

. 

The intercept shows that when the average student has completed zero semesters they will have completed 

10.0

units.

Report the slope and intercept of the regression line when the unusual point is not included and explain what it shows. If the intercept is not appropriate to? report, explain why. Select the correct choice below and fill in the answer boxes to complete your choice.

?(Round to one decimal place as? needed.)

A.

The slope shows that for each additional semester? completed, the average number of units completed will increase by 

13.7

. 

It is not appropriate to report the intercept because a student cannot complete 

negative 3.7

units.

B.

The slope shows that for each additional semester? completed, the average number of units completed will increase by 

nothing

. 

The intercept shows that when the average student has completed zero semesters they will have completed 

nothing

units.

C.

The slope shows? that, for each additional unit? completed, the average number of semesters completed will increase by 

nothing

. 

The intercept shows that when the average student has completed zero units they will have completed 

nothing

semesters.

Comment on the difference in the slope and intercept of the regression line when the unusual point is removed.

A.

When the unusual point is? removed, the intercept decreases and the slope increases.

This is the correct answer.

B.

When the unusual point is? removed, the intercept and the slope both decrease.

C.

When the unusual point is? removed, the intercept increases and the slope decreases.

D.

When the unusual point is? removed, the intercept and the slope both increase.

Question is complete. Tap on the red indicators to see incorrect answers.

      

Assume that in a sociology? class, the teacher gives a midterm exam and a final exam. Assume that the association between midterm and final scores is linear. The summary statistics are shown below.? Also, r? = 

0.75

and n? = 

26

.

   

Mean

 

Standard   deviation

 

Midterm

 

75

 

8

 

Final

 

75

         

  

8

Complete parts? (a) through? (d) below.

a. Find and report the equation of the regression line to predict the final exam score from the midterm score.

Predicted Final 

Gradeequals

18.75plus0.75

Midterm Grade

?(Type integers or decimals. Do not? round.) 

b. For a student who gets 

51

on the? midterm, predict the final exam score.

The predicted final exam grade is 

57

.

?(Round to the nearest integer as? needed.) 

c. Your answer to part? (b) should be higher than 

51

. 

?Why?

A.

The? student's final score should be higher than his or her midterm score because of regression toward the 

meanlong dash

predictor 

variables far from the mean tend to produce response variables closer to the mean.

This is the correct answer.

B.

The? student's final score should be higher than his or her midterm score because of regression toward the 

meanlong dash

scores 

tend to improve with repeated attempts.

C.

The? student's final score should be higher than his or her midterm score because of 

extrapolationlong dash

the 

score of 

51

is outside the range of the data.

D.

The? student's final score should be higher than his or her midterm score because of 

extrapolationlong dash

the 

predicted score is lower than the midterm score.

d. Consider a student who gets a 100 on the midterm. Without doing any? calculations, state whether the predicted score on the final exam would be? higher, lower, or the same as 100.

The predicted score on the final exam would be 

lower than 

100 because of 

regression toward the mean. 

Assume that in a sociology? class, the teacher gives a midterm exam and a final exam. Assume that the association between midterm and final scores is linear. The summary statistics are shown below.? Also, r? = 

0.75

and n? = 

26

.

   

Mean

 

Standard   deviation

 

Midterm

 

75

 

8

 

Final

 

75

         

  

8

Complete parts? (a) through? (d) below.

a. Find and report the equation of the regression line to predict the final exam score from the midterm score.

Predicted Final 

Gradeequals

18.75plus0.75

Midterm Grade

?(Type integers or decimals. Do not? round.) 

b. For a student who gets 

51

on the? midterm, predict the final exam score.

The predicted final exam grade is 

57

.

?(Round to the nearest integer as? needed.) 

c. Your answer to part? (b) should be higher than 

51

. 

?Why?

A.

The? student's final score should be higher than his or her midterm score because of regression toward the 

meanlong dash

predictor 

variables far from the mean tend to produce response variables closer to the mean.

This is the correct answer.

B.

The? student's final score should be higher than his or her midterm score because of regression toward the 

meanlong dash

scores 

tend to improve with repeated attempts.

C.

The? student's final score should be higher than his or her midterm score because of 

extrapolationlong dash

the 

score of 

51

is outside the range of the data.

D.

The? student's final score should be higher than his or her midterm score because of 

extrapolationlong dash

the 

predicted score is lower than the midterm score.

d. Consider a student who gets a 100 on the midterm. Without doing any? calculations, state whether the predicted score on the final exam would be? higher, lower, or the same as 100.

The predicted score on the final exam would be 

lower than 

100 because of 

regression toward the mean. 

Assume that in a sociology? class, the teacher gives a midterm exam and a final exam. Assume that the association between midterm and final scores is linear. The summary statistics are shown below.? Also, r? = 

0.75

and n? = 

26

.

   

Mean

 

Standard   deviation

 

Midterm

 

75

 

8

 

Final

 

75

         

  

8

Complete parts? (a) through? (d) below.

a. Find and report the equation of the regression line to predict the final exam score from the midterm score.

Predicted Final 

Gradeequals

18.75plus0.75

Midterm Grade

?(Type integers or decimals. Do not? round.) 

b. For a student who gets 

51

on the? midterm, predict the final exam score.

The predicted final exam grade is 

57

.

?(Round to the nearest integer as? needed.) 

c. Your answer to part? (b) should be higher than 

51

. 

?Why?

A.

The? student's final score should be higher than his or her midterm score because of regression toward the 

meanlong dash

predictor 

variables far from the mean tend to produce response variables closer to the mean.

This is the correct answer.

B.

The? student's final score should be higher than his or her midterm score because of regression toward the 

meanlong dash

scores 

tend to improve with repeated attempts.

C.

The? student's final score should be higher than his or her midterm score because of 

extrapolationlong dash

the 

score of 

51

is outside the range of the data.

D.

The? student's final score should be higher than his or her midterm score because of 

extrapolationlong dash

the 

predicted score is lower than the midterm score.

d. Consider a student who gets a 100 on the midterm. Without doing any? calculations, state whether the predicted score on the final exam would be? higher, lower, or the same as 100.

The predicted score on the final exam would be 

lower than 

100 because of 

regression toward the mean. 

A? state's recidivism rate is 

21

?%. 

This means about 

21

?% 

of released prisoners end up back in prison? (within three? years). Suppose two randomly selected prisoners who have been released are studied. Complete parts? (a) through? (c) below.

a. What is the probability that both of them go back to? prison? What assumptions must you make to calculate? this?

The probability that both of them go back to prison is 

4.4

?%.

?(Round to one decimal place as? needed.)

What assumptions must you make to calculate? this?

A.

The prisoners cannot be independent with regard to recidivism.

B.

The two prisoners cannot be selected at the same time.

C.

The prisoners must be independent with regard to recidivism.

This is the correct answer.

D.

No assumptions are necessary.

b. What is the probability that neither of them goes back to? prison?

The probability that neither of them goes back to prison is 

62.4

?%.

?(Round to one decimal place as? needed.)

c. What is the probability that at least one goes back to? prison?

The probability that at least one goes back to prison is 

37.6

?%.

?(Round to one decimal place as? needed.)

A? state's recidivism rate is 

21

?%. 

This means about 

21

?% 

of released prisoners end up back in prison? (within three? years). Suppose two randomly selected prisoners who have been released are studied. Complete parts? (a) through? (c) below.

a. What is the probability that both of them go back to? prison? What assumptions must you make to calculate? this?

The probability that both of them go back to prison is 

4.4

?%.

?(Round to one decimal place as? needed.)

What assumptions must you make to calculate? this?

A.

The prisoners cannot be independent with regard to recidivism.

B.

The two prisoners cannot be selected at the same time.

C.

The prisoners must be independent with regard to recidivism.

This is the correct answer.

D.

No assumptions are necessary.

b. What is the probability that neither of them goes back to? prison?

The probability that neither of them goes back to prison is 

62.4

?%.

?(Round to one decimal place as? needed.)

c. What is the probability that at least one goes back to? prison?

The probability that at least one goes back to prison is 

37.6

?%.

?(Round to one decimal place as? needed.)

When a certain type of thumbtack is? tossed, the probability that it lands tip up is 

30

?%, 

and the probability that it lands tip down is 

70

?%. 

All possible outcomes when two thumbtacks are tossed are listed. U means the tip is up and D means the tip is down. Complete parts? (a) through? (d) below.

  

UU

 

UD

 

DU

 

DD

a. What is the probability of getting exactly one? Down?

?P(exactly one 

?Down)equals

0.42

?(Round to two decimal places as? needed.)

b. What is the probability of getting two? Downs?

?P(two 

?Downs)equals

0.49

?(Round to two decimal places as? needed.)

c. What is the probability of at least one Down? (one or more? Downs)?

?P(at least one 

?Down)equals

0.91

?(Round to two decimal places as? needed.)

d. What is the probability of at most one Down? (one or fewer? Downs)?

?P(at most one 

?Down)equals

0.51

?(Round to two decimal places as? needed.)

  

incorrect, 5.2.25 

           

A poll asked people if college was worth the financial investment. They also asked the? respondent's gender. The table shows a summary of the responses. If a person is chosen randomly from the? group, what is the probability of selecting a person who is male or said Yes? (or both)?

   

Female

 

Male

 

All

 

 

No

 

54

42

96

      

Unsure

 

87

81

168

      

Yes

 

582

407

989

      

All

 

723

530

1253

     

What is the probability that the person from the table is? male?

0.423

?(Round to three decimal places as? needed.)

What is the probability that the person said? Yes?

0.789

?(Round to three decimal places as? needed.)

Are the event being male and the event saying Yes mutually? exclusive? Why or why? not?

A.

The events are not mutually exclusive because the probability that a person said yes given that they are male is not the same as the probability that a person is male.

B.

The events are not mutually exclusive because a person chosen could be male and say Yes.

This is the correct answer.

C.

The events are not mutually exclusive because the probability that a person is male given that they said yes is not the same as the probability that a person said yes.

D.

The events are mutually exclusive because a person chosen could be male and say Yes.

What is the probability that a person is male and said? Yes?

0.325

?(Round to three decimal places as? needed.)

To find the probability that a person is male or said? yes, why should you subtract the probability that a person is male and said Yes from the sum as shown? below?

?P(male or 

?Yes)equals

?P(male)plus?P(Yes)minus

?P(male 

and? Yes)

A.

For this specific problem? P(male and? Yes) should be subtracted out.

B.

The events are mutually exclusive so? P(Male and? Yes) has to be subtracted? out, but the value is always 0 in this case.

C.

Because any males who said yes would be counted twice if just? P(Male) and? P(Yes) were added.

This is the correct answer.

D.

Because? P(male or? Yes) is looking for people who are male or who said Yes but not both.

Perform the calculation? P(male or 

?Yes)equals

?P(male)plus?P(Yes)minus

?P(male 

and? Yes).

S