Question

  

Petroleum pollution in oceans stimulates the growth of certain bacteria. An assessment of this growth has been made by counting the bacteria in each of 5 randomly chosen specimens of ocean water (of a fixed size). The 5 counts obtained were as follows: 40, 69, 57,64, 65. What is the standard deviation of this sample of numbers? Round answer to two decimal places

Michael Phelps won five gold medals in swimming. The events he won along with his margin of victory, in seconds.

Event. Margin of victory

200

m butterfly. 0.04

200m indiv medley. 1.95

4x100m freestyle. 0.61

4x200m freestyle. 2.47

4x100m Medley. 1.29

What was the mean margin of victory?

Can you also send me how you calculated the answer

Five balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all

5balls drawn from the urn are black? Round your answer to three decimal places.

4times. What is the probability of having no

1and no

3among the rolls? Round your answer to three decimal places.

geA fair die is rolled

5times. What is the probability that a

3is obtained on at least one of the rolls? Round your answer to three decimal places.

PageAn urn contains

5orange balls and

8red balls. If Frank chooses

7balls at random from the urn, what is the probability that he will select

2orange balls and

5red balls? Round your answer to

3decimal places.

(If necessary, consult a list of formulas.)

A history class is comprised of

6female and

5male students. If the instructor of the class randomly chooses

7students from the class for an oral exam, what is the probability that

3female students and

4male students will be selected? Round your answer to

3decimal places.(If necessary, consult a list of formulas.)

PageAn urn contains

5yellow balls and

9white balls. If Vince chooses

7balls at random from the urn, what is the probability that he will select

2yellow balls and

5white balls? Round your answer to

3decimal places.

geA history class is comprised of

10female and

3male students. If the instructor of the class randomly chooses

9students from the class for an oral exam, what is the probability that

7female students and

2male students will be selected? Round your answer to

3decimal places.(If necessary, consult a list of formulas.)

The workers’ union at a particular university is quite strong. About

94

%of all workers employed by the university belong to the workers’ union. Recently, the workers went on strike, and now a local TV station plans to interview

4workers (chosen at random) at the university to get their opinions on the strike. What is the probability that exactly

2of the workers interviewed are union members?

Round your response to at least three decimal places. (If necessary, consult a list of formulas.)

eSuppose that the New England Colonials baseball team is equally likely to win a game as not to win it. If

5Colonials games are chosen at random, what is the probability that exactly

3of those games are won by the Colonials?

Round your response to at least three decimal places. (If necessary, consult a list of formulas.)

geNot all visitors to a certain company’s website are customers. In fact, the website administrator estimates that about

8

%of all visitors to the website are looking for other websites. Assuming that this estimate is correct, find the probability that, in a random sample of

4visitors to the website, exactly

3actually are looking for the website.

Round your response to at least three decimal places. (If necessary, consult a list of formulas.)

Anita’s, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food “to go”), so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita’s reports that

48

%of its customers order their food to go. If this proportion is correct, what is the probability that, in a random sample of

4customers at Anita’s, exactly

2order their food to go?

Round your response to at least three decimal places. (If necessary, consult a list of formulas.)

Suppose that the genders of the three children of a family are soon to be revealed. An outcome is represented by a string of the sort

GBB

(meaning the oldest child is a girl, the second oldest is a boy, and the youngest is a boy). The

8outcomes are listed in the table below. Note that each outcome has the same probability.

For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. (If necessary, consult a list of formulas.)Outcomes

ProbabilityBGB

BGG

GGB

BBG

BBB

GBB

GGG

GBG

Events

A girl on both the first and the last birthsTwo or more boysA girl on the first birth or the second birth (or both)

Suppose that the genders of the three children of a family are soon to be revealed. An outcome is represented by a string of the sort GBB (meaning the oldest child is a girl, the second oldest is a boy, and the youngest is a boy). The

8outcomes are listed in the table below. Note that each outcome has the same probability.
For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. (If necessary, consult a list of formulas.)Outcomes
ProbabilityBGB
BGG
GGB
BBG
BBB
GBB
GGG
GBG
Events
A girl on both the first and the last birthsTwo or more boysA girl on the first birth or the second birth (or both)
Suppose that the genders of the three children of a family are soon to be revealed. An outcome is represented by a string of the sort GBB (meaning the oldest child is a girl, the second oldest is a boy, and the youngest is a boy). The
8outcomes are listed in the table below. Note that each outcome has the same probability.
For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. (If necessary, consult a list of formulas.)Outcomes
ProbabilityBGB
BBG
BBB
GGB
GBG
GBB
BGG
GGG
Events

A boy on the first birth or the third birth (or both)More girls than boysA boy on the second birth

A coin is tossed three times. An outcome is represented by a string of the sort

HTT

(meaning a head on the first toss, followed by two tails). The

8outcomes are listed in the table below. Note that each outcome has the same probability.
For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. (If necessary, consult a list of formulas.)Outcomes

ProbabilityTTT

HTT

THH

TTH

THT

HTH

HHT

HHH

Events

Alternating heads and tails (with either coming first)Two or more headsMore heads than tails

We want to predict the selling price of a house in Newburg Park, Florida, based on the distance the house lies from the beach. Suppose that we’re given the data in the table below. These data detail the distance from the beach (

x, in miles) and the selling price (

y, in thousands of dollars) for each of a sample of fifteen homes sold in Newburg Park in the past year. The data are plotted in the scatter plot in Figure 1. Also given are the products of the distances from the beach and house prices for each of the fifteen houses. (These products, written in the column labelled “

xy,” may aid in calculations.)Distance from the beach, x

(in miles)

Selling price, y

(in thousands of dollars)xy

6.6

26

9.2

177

6.7

2

9.6

20

3.1

1949.76

7.4

305.72262.18

5.3

261.3138

4.8

9

5.3

212.3112

5.1

9

17

222.43780.8

11.9

195.72328.83

7.5

292.82196

12.1

235.62850.76

10.4

270.72815.28

15

263.53952.5

14.2

19

8.2

28

14.4

4

7.7

231.41781.78

5.1

312.91595.79

8

241.31930.4Send data

to Excel

x

5
10
15
20
y

150

200

250

300

350

0Figure 1Answer the following. Carry your intermediate computations to at least four decimal places, and round your answer as specified below. (If necessary, consult a list of formulas.)What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places.Clears your work.

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The well-known psychologist Dr. Elbod has established what he calls his Generalized Anxiety Scale (GAS). The GAS, which is a scale from

0to

10, measures the “general anxiety” of an individual, with higher GAS scores corresponding to more anxiety. (Dr. Elbod’s assessment of anxiety is based on a variety of measurements, both physiological and psychological.)We’re interested in making predictions about individuals’ sleep behavior based on their GAS scores. The bivariate data below give the GAS score (denoted by

x) and the number of hours of sleep last night (denoted by

y) for each of the fifteen adults participating in a study. A scatter plot of the data is shown in Figure 1.GAS score, x

Sleep time, y

(in hours)

9.2

6.1

7.9

6.9

2
8

7.1

6.5

3.1
6.9
6.1
8

6.4

6

8.1

5.4

1.5

8.7

9

5.9

0.9

7.2

3.8

8.2

4.1

7.3

4.8
6

3.4

7.6Send data

to Excelx

2
4
6
8
10
y
5
6
7
8
9
10

0Figure 1The value of the sample correlation coefficient

rfor these data is approximately

−

0.706.Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.)What is the value of the slope of the least-squares regression line for these data? Round your answer to at least two decimal places.What is the value of the y-intercept of the least-squares regression line for these data? Round your answer to at least two decimal places.Clears your work.

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ageBelow are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both the number of births

xper one thousand people in the population and the female life expectancy

y(in years) are given. These data are displayed in the Figure 1 scatter plot. Also given are the products of the birthrates and female life expectancies for each of the twelve countries. (These products, written in the column labelled “

xy,” may aid in calculations.)Birthrate, x

(number of births per 1000 pop.)

Female life expectancy, y

(in years)xy

30.5

64.21958.1

40.5

66.02673

27.3

73.01992.9

33.6

65.32194.08

13

72.9947.7

51.6

60.13101.16

26.4

74.31961.52

18.5

71.61324.6

45.8

58.62683.88

50.4

54.12726.64

14.4

74.71075.68

48.6

60.92959.74Send data

to Excelx
10
15
20
25
30
35
40
45
50
55
60
y
50
55
60
65
70
75
80
85

0Figure 1Answer the following. Carry your intermediate computations to at least four decimal places, and round your answer as specified below. (If necessary, consult a list of formulas.)What is the value of the slope of the least-squares regression line for these data? Round your answer to at least two decimal places.

The following data are the grades of

17students on an algebra test.79, 64, 63, 89, 63, 91, 85, 69, 75, 71, 72, 84, 90, 65, 55, 83, 85Send data

to Excel

Using the tool provided, construct a box-and-whisker plot for the data.

55

60
65
70
75
80
85
90
95

Score on algebra testClears your work.

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The following data are the numbers of local channels available in

18cities.11, 12, 13, 29, 37, 19, 34, 25, 26, 19, 14, 15, 5, 35, 32, 31, 36, 17Send data

to Excel
Using the tool provided, construct a box-and-whisker plot for the data.

Ten years ago, a psychologist specializing in male-female relationships authored a book detailing the way in which he believed couples could improve their relationships. His publisher recently was interested in the effect the book has had on married men. The publisher interviewed

64married men and asked each to rate his marriage, on a scale of

1to

20, both before reading the book and after reading the book. For each man, the difference between the two ratings was recorded. These differences are summarized in the histogram below. Note that a negative difference means that the marriage rating before reading the book was higher than the marriage rating after.35

30
25
20
15
10
5
0

Frequency4

4
32
20

04/Apr

0
4
8
12
16

Difference in marriage ratingBased on this histogram, estimate the standard deviation of the sample of

64differences.

Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.

geThe manufacturer of Doze-Off sleeping pills claims that the standard deviation of the time it takes insomniacs to fall asleep after taking the pill is no more than

5minutes. To test this claim, a consumer group performed a study involving

24adults who complained of trouble falling asleep. For each adult, the time needed to fall asleep after taking Doze-Off was recorded. The results were reported via the following histogram:15

10
5
0

Frequency2

12
6
44
8
12
16
20

Time to fall asleep (in minutes)Based on this histogram, estimate the standard deviation of the sample of

24times.

Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.
(If necessary, consult a list of formulas.)

geThe following is a list of 10 measurements.

57, 21, -48, -98, 80, -43, 21, -19, -45, 3Send data

to Excel

Suppose that these 10 measurements are respectively labeled

x
1,
x
2,

…,

x

10. (Thus,

57is labeled

x
1,

21is labeled

x

2, and so on.) Compute the following.+

−
49
Σ
=
i
1
10
x
i

geThe following is a list of 15 measurements.

22, -92, -82, -32, 91, -98, 57, 21, -48, -98, 80, -43, 21, -19, -45Send data

to Excel

Suppose that these 15 measurements are respectively labeled

x
1,
x
2,
…,
x

15. (Thus,

22is labeled

x
1,
−

92is labeled

x

2, and so on.) Compute the following.Σ

=
i
1
15
x
i

2Round your answer to at least two decimal places.

A movie studio wishes to determine the relationship between the revenue from rental of comedies on DVD and videotape and the revenue generated from the theatrical release of such movies. The studio has the following bivariate data from a sample of fifteen comedies released over the past five years. These data give the revenue

xfrom theatrical release

(in millions of dollars)

and the revenue

yfrom DVD and videotape rentals (in millions of dollars) for each of the fifteen movies. Also shown are the scatter plot and the least-squares regression line for the data. The equation for this line is

=
y
+
3.4

0.15

x.

Theater revenue, x

(in millions of dollars)

Rental revenue, y

(in millions of dollars)

60.8

16.1

25.8

8.1

36.6

11.9

21.1

5.4

48.5

15.7

6.2

2.2

30.6

5.4

27.8

3

45.5

6.7

27.2

12.4

25.2

7.4

66.2

10.2

13.1

9.9

15.4

2.2

62.7

9.6Send data

to Excelx
10
20
30
40
50
60
70
y
2
4
6
8
10
12
14
16
18

0Figure 1Based on the studio’s data and the regression line, answer the following:1. Fill in the blank: For these data, values for theater revenue that are less than the mean of the values for theater revenue tend to be paired with values for rental revenue that are _____ the mean of the values for rental revenue.2. According to the regression equation, for an increase of one million dollars in theater revenue, there is a corresponding increase of how many million dollars in rental revenue?3. What was the observed rental revenue (in millions of dollars) when the theater revenue was 27.2 million dollars?4. From the regression equation, what is the predicted rental revenue (in millions of dollars) when the theater revenue is 27.2 million dollars? (Round your answer to at least one decimal place.)Clears your work.

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An Instructor grades exams 20%, term paper 20% and final exam 60%. A student had grades of 83,72 and 98 respectively for exams, term paper and final exam. find the students final average. use the weighted mean

The workers’ union at a particular university is quite strong. About
96
%of all workers employed by the university belong to the workers’ union. Recently, the workers went on strike, and now a local TV station plans to interview
4workers (chosen at random) at the university to get their opinions on the strike. What is the probability that exactly

3of the workers interviewed are union members?

Round your response to at least three decimal places. (If necessary, consult a list of formulas.)