Statistics 2018 | Statistics homework help

  

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.

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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.

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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).

Suppose a randomized experiment is conducted to test whether loud music interferes with memorizing numbers. There are 10 participants. Each participant should have a​ 50% chance of being assigned to the experimental group​ (memorizes numbers while music​ plays) and a​ 50% chance of being assigned to the control group​ (memorizes numbers with no​ music). Let the digits​ 0, 1,​ 2, 3, and 4 represent assignment to the experimental group​ (music) and the digits​ 5, 6,​ 7, 8, and 9 represent assignment to the control group. Use the random number table to simulate the 10 assignments. Begin with the first digit in the third row of the random number table. Complete parts​ (a) through​ (c) below.

LOADING…

Click the icon to view the random number table.

  

a.

Write the sequence of 10 random   digits. For each number write M under it if it represents a participant   randomized to the music group and C if it represents a student randomized to   the control group.

List the numbers in order as seen in the random number table beginning with the first digit in the third row.

The sequence is 

3

​,6​,3​,9​,4​,8​,7​,7​,3​,0

.

Write the sequence participant assignment. Write M if it represents a participant randomized to the music group and C if it represents a student randomized to the control group.

The assignment sequence is 

​, 

​, 

​, 

​, 

​, 

​, 

​, 

​, 

​, 

.

b. What percentage of the 10 participants were assigned to the music​ group?

50

​%

  

c. 

Would it be appropriate to assign   all the even numbers​ (0, 2,​ 4, 6,​ 8) to the music group and all the odd   numbers​ (1, 3,​ 5, 7,​ 9) to the control​ group? Why or why​ not?

A.

It would not be appropriate. Any randomized experiment must assign participants as a block of random numbers. 

B.

It would not be appropriate. The same number of participants would not be assigned to each group.

C.

It would be appropriate. As half the numbers are even and half the numbers are odd each participant would still have a​ 50% chance to be assigned to each group.

This is the correct answer.

D.

It would not be appropriate. The numbers do not all have the same probability of occurring.

Suppose a randomized experiment is conducted to test whether loud music interferes with memorizing numbers. There are 10 participants. Each participant should have a​ 50% chance of being assigned to the experimental group​ (memorizes numbers while music​ plays) and a​ 50% chance of being assigned to the control group​ (memorizes numbers with no​ music). Let the digits​ 0, 1,​ 2, 3, and 4 represent assignment to the experimental group​ (music) and the digits​ 5, 6,​ 7, 8, and 9 represent assignment to the control group. Use the random number table to simulate the 10 assignments. Begin with the first digit in the third row of the random number table. Complete parts​ (a) through​ (c) below.

LOADING…

Click the icon to view the random number table.

  

a.

Write the sequence of 10 random   digits. For each number write M under it if it represents a participant   randomized to the music group and C if it represents a student randomized to   the control group.

List the numbers in order as seen in the random number table beginning with the first digit in the third row.

The sequence is 

3

​,6​,3​,9​,4​,8​,7​,7​,3​,0

.

Write the sequence participant assignment. Write M if it represents a participant randomized to the music group and C if it represents a student randomized to the control group.

The assignment sequence is 

​, 

​, 

​, 

​, 

​, 

​, 

​, 

​, 

​, 

.

b. What percentage of the 10 participants were assigned to the music​ group?

50

​%

  

c. 

Would it be appropriate to assign   all the even numbers​ (0, 2,​ 4, 6,​ 8) to the music group and all the odd   numbers​ (1, 3,​ 5, 7,​ 9) to the control​ group? Why or why​ not?

A.

It would not be appropriate. Any randomized experiment must assign participants as a block of random numbers. 

B.

It would not be appropriate. The same number of participants would not be assigned to each group.

C.

It would be appropriate. As half the numbers are even and half the numbers are odd each participant would still have a​ 50% chance to be assigned to each group.

This is the correct answer.

D.

It would not be appropriate. The numbers do not all have the same probability of occurring.

According to data for a​ population, 3-year-old boys have a mean height of 

38

inches and a standard deviation of 

2

inches. Assume the distribution is approximately Normal. Complete parts a and 

b.

  

a. nbsp

Find the percentile measure for a height of 

34

  

inches for a​ 3-year-old boy.

A height of 

34

inches corresponds to the 

2

nd 

percentile.

​(Round down to the nearest percentile as​ needed.)

  

b. nbsp

If this​ 3-year-old boy grows up to be a man with a height at the same​ percentile, what will his height​ be? Use a population mean of 

70

inches and a population standard deviation of 

3

  

inches.

His height will be 

64.0

inches.

​(Round to the nearest tenth as​ needed.)

  

incorrect, 6.2.45 

           

The mean quantitative score on a standardized test for female​ college-bound high school seniors was 

600

The scores are approximately Normally distributed with a population standard deviation of 

50

A scholarship committee wants to give awards to​ college-bound women who score at the 

96

th 

percentile or above on the test. What score does an applicant​ need? Complete parts​ (a) through​ (g) below.

Click here to view page 1 of the Standard Normal Table. 

LOADING…

Click here to view page 2 of the Standard Normal Table. 

LOADING…

a. Will the test score be above the mean or below​ it? Explain.

A.

The test score will be below the mean because the 

96

th 

percentile represents the test score that is higher than 

96

​% 

of the other scores.

B.

The test score will be below the mean because the 

96

th 

percentile represents the test score that is lower than 

96

​% 

of the other scores.

C.

The test score will be above the mean because the 

96

th 

percentile represents the test score that is lower than 

96

​% 

of the other scores.

D.

The test score will be above the mean because the 

96

th 

percentile represents the test score that is higher than 

96

​% 

of the other scores.

This is the correct answer.

  

b. Label the curve with integer​   z-scores. The tick marks represent the position of integer​ z-scores from 

minus

      

to 3.

A graph has a horizontal axis   labeled with 7 evenly spaced ticks and a vertical axis labeled Density. A   symmetrical bell-shaped curve is drawn such that the ends of the curve meet   the horizontal axis near the first and seventh ticks, and the highest point of   the curve occurs at the fourth tick. The first tick aligns with the first   answer box, the second tick aligns with the second answer box, the third tick   aligns with the third answer box, the fourth tick aligns with an axis label   of 0 and an additional label of 600, the fifth tick aligns with the fourth   answer box, the sixth tick aligns with the fifth answer box, and the seventh   tick aligns with an axis label of 3 and an additional label of 750. 

                                 

negative 3

             

negative 2

negative 1

  

0

1

2

  

3

      

600

    

750

    

c. The 

96

th 

percentile has 

96

​% 

of the area to the left because it is higher than 

96

​% 

of the scores. The table above gives the areas to the left of​ z-scores. Therefore, we look for 

0.9600

in the interior part of the table. Use the Normal table given above to locate the area closest to 

0.9600

Then report the​ z-score for that area.

zequals

1.75

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

d. Add that​ z-score to the​ sketch, and draw a vertical line above it through the curve. Shade the area corresponding to the data values below the 

96

th 

percentile. Select the correct choice below and fill in the answer box to complete your choice.

​(Type an integer or a​ decimal.)

A.

A graph has a horizontal axis labeled with 7 evenly spaced ticks. A symmetrical bell-shaped curve is drawn such that the ends of the curve meet the horizontal axis near the first and seventh ticks, and the highest point of the curve occurs at the fourth tick. The first five ticks, from left to right, align with the following axis labels: negative 3, negative 2, negative 1, 0, and 1; the sixth tick is not labeled, and the seventh tick aligns with an axis label of 3. To the near left of the sixth tick is a vertical line segment extending from the horizontal axis to the curve. This vertical line segment separates a shaded region on its left and a non-shaded region on its right. An answer box is located just below the vertical line segment. 

  

minus

 

3

minus

      

  

2

minus

  

1

0

1

1.75

  

3

B.

A graph has a horizontal axis labeled with 7 evenly spaced ticks. A symmetrical bell-shaped curve is drawn such that the ends of the curve meet the horizontal axis near the first and seventh ticks, and the highest point of the curve occurs at the fourth tick. The first five ticks, from left to right, align with the following axis labels: negative 3, negative 2, negative 1, 0, and 1; the sixth tick is not labeled, and the seventh tick aligns with an axis label of 3. To the near left of the sixth tick is a vertical line segment extending from the horizontal axis to the curve. This vertical line segment separates a non-shaded region on its left and a shaded region on its right. An answer box is located just below the vertical line segment. 

  

minus

 

3

minus

      

  

2

minus

  

1

0

1

nothing

  

3

e. Find the test score that corresponds to the​ z-score. The score should be z standard deviations above the​ mean, so 

xequals

mupluszsigma

.

xequals

688

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

f. Add the test score on the sketch. 

Select the correct choice below and fill in the answer box to complete your choice.

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

A.

A graph has a horizontal axis labeled with 7 evenly spaced ticks. A symmetrical bell-shaped curve is drawn such that the ends of the curve meet the horizontal axis near the first and seventh ticks, and the highest point of the curve occurs at the fourth tick. The fourth tick has axis label 600 and the seventh tick has axis label 750; none of the other ticks have labels. To the near left of the sixth tick is a vertical line segment extending from the horizontal axis to the curve. This vertical line segment separates a shaded region on its left and a non-shaded region on its right. An answer box is located just below the vertical line segment. 

     

600

  

688

750

B.

A graph has a horizontal axis labeled with 7 evenly spaced ticks. A symmetrical bell-shaped curve is drawn such that the ends of the curve meet the horizontal axis near the first and seventh ticks, and the highest point of the curve occurs at the fourth tick. The fourth tick has axis label 600 and the seventh tick has axis label 750; none of the other ticks have labels. To the near left of the sixth tick is a vertical line segment extending from the horizontal axis to the curve. This vertical line segment separates a non-shaded region on its left and a shaded region on its right. An answer box is located just below the vertical line segment. 

     

600

  

nothing

750

g.​ Finally, write a sentence stating what you found.

An applicant would need a score of 

at least 

688

to be in the 

96

th 

percentile or above.

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

       

incorrect, 6.2.38 

              

Assume for this question that college​ women’s heights are approximately Normally distributed with a mean of 

64.6

inches and a standard deviation of 

2.4

inches. Complete parts​ (a) through​ (d) below.

LOADING…

Click the icon to view a data table from a sample of 

129

college women.

a. Find the percentage of women who should have heights of 

63.5

inches or less. Draw a Normal curve. Choose the correct graph below.

A.

0-33    z-scoreDensity

A coordinate system has a horizontal axis labeled from less than negative 3 to 3 plus in intervals of 1 and a vertical axis labeled “Density.” A Normal curve extends between the left and right edges of the graph with a peak at horizontal coordinate 0. A vertical line segment, running from the horizontal axis to the curve, is plotted at approximate horizontal coordinate negative 0.46. The area under the curve to the left of the vertical line is shaded.

This is the correct answer.

B.

0-33    z-scoreDensity

A coordinate system has a horizontal axis labeled from less than negative 3 to 3 plus in intervals of 1 and a vertical axis labeled “Density.” A Normal curve extends between the left and right edges of the graph with a peak at horizontal coordinate 0. A vertical line segment, running from the horizontal axis to the curve, is plotted at approximate horizontal coordinate 59 comma 60 comma 61 comma 62 comma 63 comma 64 comma 65 comma 66 comma 67 comma 68 comma 69 comma 70 comma 71 comma 72. The area under the curve to the left of the vertical line is shaded.

C.

0-33    z-scoreDensity

A coordinate system has a horizontal axis labeled from less than negative 3 to 3 plus in intervals of 1 and a vertical axis labeled “Density.” A Normal curve extends between the left and right edges of the graph with a peak at horizontal coordinate 0. A vertical line segment, running from the horizontal axis to the curve, is plotted at approximate horizontal coordinate negative 0.46. The area under the curve to the right of the vertical line is shaded.

D.

0-33    z-scoreDensity

A coordinate system has a horizontal axis labeled from less than negative 3 to 3 plus in intervals of 1 and a vertical axis labeled “Density.” A Normal curve extends between the left and right edges of the graph with a peak at horizontal coordinate 0. A vertical line segment, running from the horizontal axis to the curve, is plotted at approximate horizontal coordinate 0.46. The area under the curve to the right of the vertical line is shaded.

The percentage of women who should have heights of 

63.5

inches or less is 

32.3

​%.

​(Type an integer or decimal rounded to one decimal place as​ needed.)

b. In a sample of 

129

​women, according to the probability obtained in part​ (a), how many should have heights of 

63.5

inches or​ less?

In a sample of 

129

​women, 

41.71

should have heights of 

63.5

inches or less.

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

c. The attached table shows the frequencies of heights for a sample of 

129

women. Count the women who appear to have heights of 

63

inches or less by looking at the table. 

The number of women in the sample that have a height of 

63

inches or less is 

41

.

​(Type a whole​ number.) 

d. Are the answers to parts b and c the same or​ different? Explain.

A.

The answers are very different. This distribution is a good approximation for this sample.

B.

The answers are very close. This distribution is a good approximation for this sample.

This is the correct answer.

C.

The answers are very close. This distribution is not a good approximation for this sample.

D.

The answers are very different. This distribution is not a good approximation for this sample.

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

      

You​ answered: 

nothing

  

incorrect, 6.2.32 

           

The distribution of red blood cell counts is different for 

men

and 

women

in a certain population. For​ both, the distribution is approximately Normal. For 

men

​, 

the middle​ 95% range from 

4.6

to 

5.8

million cells per​ microliter, and for 

women

​, 

the middle​ 95% have red blood cell counts between 

3.6

and 

4.8

million cells per microliter. Complete parts​ (a) and​ (b) below.

a. What is the mean for the 

women

​? 

Explain your reasoning.

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

A.

The mean is 

nothing

million. Since the mode of the Normal distribution is equal to its​ mean, the mean is equal to the distance between the boundary values for the middle​ 95%.

B.

The mean is 

nothing

million. Since the Normal distribution is symmetric about its​ mean, the mean is the lower of the boundary values for the middle​ 95%.

C.

The mean is 

4.20

million. Since the Normal distribution is symmetric about its​ mean, the mean is right in the​ middle, which is the average of the boundary values for the middle​ 95%.

D.

The mean is 

nothing

million. Since the mode of the Normal distribution is equal to its​ mean, the mean is the higher of the boundary values for the middle​ 95%.

b. Find the standard deviation for the 

women

Explain your reasoning.

The standard deviation is 

0.31

million. The Empirical Rule states that about​ 95% of the data fall within 

two 

standard​ deviation(s) of the mean. The middle​ 95% of values spans 

four 

standard​ deviation(s). The standard deviation is found by dividing the range of the middle​ 95% by 

4.00

.

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

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

       

incorrect, 6.2.31 

              

The distribution of red blood cell counts is different for 

men

and 

women

in a certain population. For​ both, the distribution is approximately Normal. For 

men

​, 

the middle​ 95% range from 

4.7

to 

6.3

million cells per​ microliter, and for 

women

​, 

the middle​ 95% have red blood cell counts between 

3.7

and 

4.5

million cells per microliter. Complete parts​ (a) and​ (b) below.

a. What is the mean for the 

men

​? 

Explain your reasoning. Select the correct choice below and fill in the answer box to complete your choice.

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

A.

The mean is 

nothing

million. Since the mode of the Normal distribution is equal to its​ mean, the mean is equal to the distance between the boundary values for the middle​ 95%.

B.

The mean is 

nothing

million. Since the Normal distribution is symmetric about its​ mean, the mean is the lower of the boundary values for the middle​ 95%.

C.

The mean is 

nothing

million. Since the mode of the Normal distribution is equal to its​ mean, the mean is the higher of the boundary values for the middle​ 95%.

D.

The mean is 

5.50

million. Since the Normal distribution is symmetric about its​ mean, the mean is right in the​ middle, which is the average of the boundary values for the middle​ 95%.

b. Find the standard deviation for the 

men

Explain your reasoning.

The standard deviation is 

0.41

million. The Empirical Rule states that about​ 95% of the data fall within 

two 

standard​ deviation(s) of the mean. The middle​ 95% of values spans 

four 

standard​ deviation(s). The standard deviation is found by dividing the range of the middle​ 95% by 

4.00

.

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

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

       

incorrect, 6.2.25 

              

According to the​ data, the mean quantitative score on a standardized test for female​ college-bound high school seniors was 

500

The scores are approximately Normally distributed with a population standard deviation of 

100

What percentage of the female​ college-bound high school seniors had scores above 

628

​? 

Answer this question by completing parts​ (a) through​ (g) below.

Click here to view page 1 of the Standard Normal Table. 

LOADING…

Click here to view page 2 of the Standard Normal Table. 

LOADING…

a. Find the​ z-score for a standardized test score of 

628

zequals

1.28

​(Type an integer or a decimal. Do not​ round.)

  

b. Label the Normal curve with   integer​ z-scores. The tick marks represent the position of integer​ z-scores   from 

minus

to 3. Why is the test score of 

500

directly above the​ z-score of​ 0?

A.

Because the mean is equal to the desired test score.

B.

Because a​ z-score of 0 corresponds to the desired test score.

C.

Because the mean corresponds to a​ z-score of 0.

This is the correct answer.

  

D.

Because a​ z-score of 0   corresponds to the population standard deviation.

  

0-33    Density500

A coordinate system has a   horizontal axis labeled from less than negative 3 to 3 plus in intervals of 1   and a vertical axis labeled “Density.” A Normal curve extends between the   left and right edges of the graph with a peak at horizontal coordinate 0.   Above the horizontal coordinate 0 is the label “500.”

c. Sketch a copy of the curve with standardized test score labels on the horizontal axis.

A.

0-33    Density

font size decreased by 3 200

font size decreased by 3 300

font size decreased by 3 400

font size decreased by 3 500

font size decreased by 3 600

font size decreased by 3 700

font size decreased by 3 800

A coordinate system has a horizontal axis labeled from less than negative 3 to 3 plus in intervals of 1 and a vertical axis labeled “Density.” A Normal curve extends between the left and right edges of the graph with a peak at horizontal coordinate 0. Above the horizontal axis labels is a second row of labels that align with the horizontal axis labels as follows: negative 3, 200; negative 2, 300; negative 1, 400; 0, 500; 1, 600; 2, 700; 3, 800. The middle label, 500, is highlighted.

This is the correct answer.

B.

0-33    Density

font size decreased by 3 negative 100

font size decreased by 3 100

font size decreased by 3 300

font size decreased by 3 500

font size decreased by 3 700

font size decreased by 3 900

font size decreased by 3 1100

A coordinate system has a horizontal axis labeled from less than negative 3 to 3 plus in intervals of 1 and a vertical axis labeled “Density.” A Normal curve extends between the left and right edges of the graph with a peak at horizontal coordinate 0. Above the horizontal axis labels is a second row of labels that align with the horizontal axis labels as follows: negative 3, negative 100; negative 2, 100; negative 1, 300; 0, 500; 1, 700; 2, 900; 3, 1100. The middle label, 500, is highlighted.

C.

0-33    Density

font size decreased by 3 350

font size decreased by 3 400

font size decreased by 3 450

font size decreased by 3 500

font size decreased by 3 550

font size decreased by 3 600

font size decreased by 3 650

A coordinate system has a horizontal axis labeled from less than negative 3 to 3 plus in intervals of 1 and a vertical axis labeled “Density.” A Normal curve extends between the left and right edges of the graph with a peak at horizontal coordinate 0. Above the horizontal axis labels is a second row of labels that align with the horizontal axis labels as follows: negative 3, 350; negative 2, 400; negative 1, 450; 0, 500; 1, 550; 2, 600; 3, 650. The middle label, 500, is highlighted.

d. Draw a vertical line through the curve at the location of 

628

Shade the area that represents the percentage of students that had scores above 

628

.

A.

0-33    Density

A coordinate system has a horizontal axis labeled from less than negative 3 to 3 plus in intervals of 1 and a vertical axis labeled “Density.” A Normal curve extends between the left and right edges of the graph with a peak at horizontal coordinate 0. A vertical line segment, running from the horizontal axis to the curve, is plotted at approximate horizontal coordinate negative 1.3. The area under the curve to the right of the vertical line is shaded.

B.

0-33    Density

A coordinate system has a horizontal axis labeled from less than negative 3 to 3 plus in intervals of 1 and a vertical axis labeled “Density.” A Normal curve extends between the left and right edges of the graph with a peak at horizontal coordinate 0. A vertical line segment, running from the horizontal axis to the curve, is plotted at approximate horizontal coordinate 1.3. The area under the curve to the right of the vertical line is shaded.

This is the correct answer.

C.

0-33    Density

A coordinate system has a horizontal axis labeled from less than negative 3 to 3 plus in intervals of 1 and a vertical axis labeled “Density.” A Normal curve extends between the left and right edges of the graph with a peak at horizontal coordinate 0. A vertical line segment, running from the horizontal axis to the curve, is plotted at approximate horizontal coordinate 1.3. The area under the curve to the left of the vertical line is shaded.

D.

0-33    Density

A coordinate system has a horizontal axis labeled from less than negative 3 to 3 plus in intervals of 1 and a vertical axis labeled “Density.” A Normal curve extends between the left and right edges of the graph with a peak at horizontal coordinate 0. A vertical line segment, running from the horizontal axis to the curve, is plotted at approximate horizontal coordinate negative 1.3. The area under the curve to the left of the vertical line is shaded.

e. Use the Normal table to find the area to the left of the​ z-score that was obtained from a standardized test score of 

628

.

The area to the left of the​ z-score is 

0.8997

​(Round to four decimal places as​ needed.) 

f. Find the area to the right of the​ z-score.

The area to the right of the​ z-score is 

0.1003

​(Round to four decimal places as​ needed.) 

g. What percentage of the female​ college-bound high school seniors had scores above 

628

​?

Approximately 

10.03

​% 

of the female​ college-bound high school seniors had scores above 

628

.

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

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

      

You​ answered: 

nothing

  

incorrect, 6.2.21 

           

Use technology to find the indicated area under the standard Normal curve. Include an appropriately labeled sketch of the Normal curve and shade the appropriate region.

a. Find the probability that a​ z-score will be 

0.45

or less.

b. Find the probability that a​ z-score will be 

0.45

or more.

c. Find the probability that a​ z-score will be between 

negative 1.5

and 

negative 1.05

.

a. Which graph below shows the probability that a​ z-score is 

0.45

or​ less?

A.

-0.450.45

A graph contains a Normal curve, plotted over a horizontal axis, which extends between the left and right edges of the graph and has a peak at the horizontal center. Approximately 40% of the way from the left and right edges of the graph, two vertical line segments with respective labeled horizontal coordinates negative 0.45 and 0.45 extend from the horizontal axis to the curve. The area below the curve to the left of the segment at negative 0.45 and the area below the curve to the right of the segment at 0.45 are shaded.

B.

0.45

A graph contains a Normal curve, plotted over a horizontal axis, which extends between the left and right edges of the graph and has a peak at the horizontal center. Approximately 40% of the way from the graph’s right edge, a vertical line segment with labeled horizontal coordinate 0.45 extends from the horizontal axis to the curve. The area below the curve and to the left of the vertical line segment is shaded.

This is the correct answer.

C.

0.45

A graph contains a Normal curve, plotted over a horizontal axis, which extends between the left and right edges of the graph and has a peak at the horizontal center. Approximately 40% of the way from the graph’s right edge, a vertical line segment with labeled horizontal coordinate 0.45 extends from the horizontal axis to the curve. The area below the curve and to the right of the vertical line segment is shaded.

D.

-0.450.45

A graph contains a Normal curve, plotted over a horizontal axis, which extends between the left and right edges of the graph and has a peak at the horizontal center. Approximately 40% of the way from the left and right edges of the graph, two vertical line segments with respective labeled horizontal coordinates negative 0.45 and 0.45 extend from the horizontal axis to the curve. The area below the curve between the segment at negative 0.45 and the segment at 0.45 is shaded.

The probability that a​ z-score will be 

0.45

or less is 

0.6736

​(Round to four decimal places as​ needed.)

b. Which graph below shows the probability that a​ z-score is 

0.45

or​ more?

A.

-0.450.45

A graph contains a Normal curve, plotted over a horizontal axis, which extends between the left and right edges of the graph and has a peak at the horizontal center. Approximately 40% of the way from the left and right edges of the graph, two vertical line segments with respective labeled horizontal coordinates negative 0.45 and 0.45 extend from the horizontal axis to the curve. The area below the curve between the segment at negative 0.45 and the segment at 0.45 is shaded.

B.

0.45

A graph contains a Normal curve, plotted over a horizontal axis, which extends between the left and right edges of the graph and has a peak at the horizontal center. Approximately 40% of the way from the graph’s right edge, a vertical line segment with labeled horizontal coordinate 0.45 extends from the horizontal axis to the curve. The area below the curve and to the left of the vertical line segment is shaded.

C.

-0.450.45

A graph contains a Normal curve, plotted over a horizontal axis, which extends between the left and right edges of the graph and has a peak at the horizontal center. Approximately 40% of the way from the left and right edges of the graph, two vertical line segments with respective labeled horizontal coordinates negative 0.45 and 0.45 extend from the horizontal axis to the curve. The area below the curve to the left of the segment at negative 0.45 and the area below the curve to the right of the segment at 0.45 are shaded.

D.

0.45

A graph contains a Normal curve, plotted over a horizontal axis, which extends between the left and right edges of the graph and has a peak at the horizontal center. Approximately 40% of the way from the graph’s right edge, a vertical line segment with labeled horizontal coordinate 0.45 extends from the horizontal axis to the curve. The area below the curve and to the right of the vertical line segment is shaded.

This is the correct answer.

The probability that a​ z-score will be 

0.45

or more is 

0.3264

​(Round to four decimal places as​ needed.)

c. Which graph below shows the probability that a​ z-score is between 

negative 1.5

and 

negative 1.05

​?

A.

-1.5-1.05

A graph contains a Normal curve, plotted over a horizontal axis, which extends between the left and right edges of the graph and has a peak at the horizontal center. Approximately 25% and 30% of the way from the graph’s left edge, two vertical line segments with respective labeled horizontal coordinates negative 1.5 and negative 1.05 extend from the horizontal axis to the curve. The area below the curve to the left of the segment at negative 1.5 and the area below the curve to the right of the segment at negative 1.05 are shaded.

B.

-1.5-1.05

A graph contains a Normal curve, plotted over a horizontal axis, which extends between the left and right edges of the graph and has a peak at the horizontal center. Approximately 25% and 30% of the way from the graph’s left edge, two vertical line segments with respective labeled horizontal coordinates negative 1.5 and negative 1.05 extend from the horizontal axis to the curve. The area to below the curve to the right of the segment at negative 1.5 is shaded.

C.

-1.5-1.05

A graph contains a Normal curve, plotted over a horizontal axis, which extends between the left and right edges of the graph and has a peak at the horizontal center. Approximately 25% and 30% of the way from the graph’s left edge, two vertical line segments with respective labeled horizontal coordinates negative 1.5 and negative 1.05 extend from the horizontal axis to the curve. The area below the curve between the segment at negative 1.5 and the segment at negative 1.05 is shaded.

This is the correct answer.

D.

-1.5-1.05

A graph contains a Normal curve, plotted over a horizontal axis, which extends between the left and right edges of the graph and has a peak at the horizontal center. Approximately 25% and 30% of the way from the graph’s left edge, two vertical line segments with respective labeled horizontal coordinates negative 1.5 and negative 1.05 extend from the horizontal axis to the curve. The area below the curve to the left of the segment at negative 1.05 is shaded.

The probability that a​ z-score will be between 

negative 1.5

and 

negative 1.05

is 

0.0801

.

​(Round to four decimal places as​ needed.)

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

       

incorrect, 6.1-8 

              

  

Determine whether the following is   a probability distribution. If​ not, identify the requirement that is not   satisfied.

If a person is randomly selected   from a certain​ town, the probability distribution for the​ number, x, of   siblings is as described in the accompanying table.

Start 7 By 2 Table 1st Row 1st   Column x 2nd Column Upper P left parenthesis x right parenthesis 2nd Row 1st   Column 0 2nd Column 0.24 3rd Row 1st Column 1 2nd Column 0.27 4st Row 1st   Column 2 2nd Column 0.25 5st Row 1st Column 3 2nd Column 0.13 6st Row 1st   Column 4 2nd Column 0.05 7st Row 1st Column 5 2nd Column 0.03 EndTable

                 

    

    

    

    

    

A.

Yes

B.

No

This is the correct answer.

C.

​Can’t be determined with the given information

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

      

You​ answered: 

nothing

  

incorrect, 6.2.55 

           

The average birth weight of domestic cats is about 

3

ounces. Assume that the distribution of birth weights is Normal with a standard deviation of 

0.4

ounce.

a. Find the birth weight of cats at the 

90

th 

percentile.

b. Find the birth weight of cats at the 

10

th 

percentile.

a. The birth weight of cats at the 

90

th 

percentile is 

3.51

ounces.

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

b. The birth weight of cats at the 

10

th 

percentile is 

2.49

ounces.

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

According to data for a​ population, 3-year-old boys have a mean height of 

38

inches and a standard deviation of 

2

inches. Assume the distribution is approximately Normal. Complete parts a and 

b.

  

a. nbsp

Find the percentile measure for a height of 

42

  

inches for a​ 3-year-old boy.

A height of 

42

inches corresponds to the 

97

th 

percentile.

​(Round down to the nearest percentile as​ needed.)

  

b. nbsp

If this​ 3-year-old boy grows up to be a man with a height at the same​ percentile, what will his height​ be? Use a population mean of 

70

inches and a population standard deviation of 

3

  

inches.

His height will be 

76.0

inches.

​(Round to the nearest tenth as​ needed.)

Assume college women have heights with the following distribution​ (inches): 

​N(65

​, 

1.6

​). 

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

a. Find the height at the 75th percentile.

The 75th percentile is 

66.1

.

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

b. Find the height at the 25th percentile.

The 25th percentile is 

63.9

.

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

c. Find the interquartile range for heights.

The interquartile range is 

2.2

.

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

d. Is the interquartile range larger or smaller than the standard​ deviation?

The interquartile range is 

larger 

than the standard deviation.

Assume college women have heights with the following distribution​ (inches): 

​N(65

​, 

1.6

​). 

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

a. Find the height at the 75th percentile.

The 75th percentile is 

66.1

.

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

b. Find the height at the 25th percentile.

The 25th percentile is 

63.9

.

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

c. Find the interquartile range for heights.

The interquartile range is 

2.2

.

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

d. Is the interquartile range larger or smaller than the standard​ deviation?

The interquartile range is 

larger 

than the standard deviation.

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