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  1. Preface
  2. 1 Sampling and Data
    1. Introduction
    2. 1.1 Definitions of Statistics, Probability, and Key Terms
    3. 1.2 Data, Sampling, and Variation in Data and Sampling
    4. 1.3 Frequency, Frequency Tables, and Levels of Measurement
    5. 1.4 Experimental Design and Ethics
    6. 1.5 Data Collection Experiment
    7. 1.6 Sampling Experiment
    8. Key Terms
    9. Chapter Review
    10. Practice
    11. Homework
    12. Bringing It Together: Homework
    13. References
    14. Solutions
  3. 2 Descriptive Statistics
    1. Introduction
    2. 2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
    3. 2.2 Histograms, Frequency Polygons, and Time Series Graphs
    4. 2.3 Measures of the Location of the Data
    5. 2.4 Box Plots
    6. 2.5 Measures of the Center of the Data
    7. 2.6 Skewness and the Mean, Median, and Mode
    8. 2.7 Measures of the Spread of the Data
    9. 2.8 Descriptive Statistics
    10. Key Terms
    11. Chapter Review
    12. Formula Review
    13. Practice
    14. Homework
    15. Bringing It Together: Homework
    16. References
    17. Solutions
  4. 3 Probability Topics
    1. Introduction
    2. 3.1 Terminology
    3. 3.2 Independent and Mutually Exclusive Events
    4. 3.3 Two Basic Rules of Probability
    5. 3.4 Contingency Tables
    6. 3.5 Tree and Venn Diagrams
    7. 3.6 Probability Topics
    8. Key Terms
    9. Chapter Review
    10. Formula Review
    11. Practice
    12. Bringing It Together: Practice
    13. Homework
    14. Bringing It Together: Homework
    15. References
    16. Solutions
  5. 4 Discrete Random Variables
    1. Introduction
    2. 4.1 Probability Distribution Function (PDF) for a Discrete Random Variable
    3. 4.2 Mean or Expected Value and Standard Deviation
    4. 4.3 Binomial Distribution
    5. 4.4 Geometric Distribution
    6. 4.5 Hypergeometric Distribution
    7. 4.6 Poisson Distribution
    8. 4.7 Discrete Distribution (Playing Card Experiment)
    9. 4.8 Discrete Distribution (Lucky Dice Experiment)
    10. Key Terms
    11. Chapter Review
    12. Formula Review
    13. Practice
    14. Homework
    15. References
    16. Solutions
  6. 5 Continuous Random Variables
    1. Introduction
    2. 5.1 Continuous Probability Functions
    3. 5.2 The Uniform Distribution
    4. 5.3 The Exponential Distribution
    5. 5.4 Continuous Distribution
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  7. 6 The Normal Distribution
    1. Introduction
    2. 6.1 The Standard Normal Distribution
    3. 6.2 Using the Normal Distribution
    4. 6.3 Normal Distribution (Lap Times)
    5. 6.4 Normal Distribution (Pinkie Length)
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  8. 7 The Central Limit Theorem
    1. Introduction
    2. 7.1 The Central Limit Theorem for Sample Means (Averages)
    3. 7.2 The Central Limit Theorem for Sums
    4. 7.3 Using the Central Limit Theorem
    5. 7.4 Central Limit Theorem (Pocket Change)
    6. 7.5 Central Limit Theorem (Cookie Recipes)
    7. Key Terms
    8. Chapter Review
    9. Formula Review
    10. Practice
    11. Homework
    12. References
    13. Solutions
  9. 8 Confidence Intervals
    1. Introduction
    2. 8.1 A Single Population Mean using the Normal Distribution
    3. 8.2 A Single Population Mean using the Student t Distribution
    4. 8.3 A Population Proportion
    5. 8.4 Confidence Interval (Home Costs)
    6. 8.5 Confidence Interval (Place of Birth)
    7. 8.6 Confidence Interval (Women's Heights)
    8. Key Terms
    9. Chapter Review
    10. Formula Review
    11. Practice
    12. Homework
    13. References
    14. Solutions
  10. 9 Hypothesis Testing with One Sample
    1. Introduction
    2. 9.1 Null and Alternative Hypotheses
    3. 9.2 Outcomes and the Type I and Type II Errors
    4. 9.3 Distribution Needed for Hypothesis Testing
    5. 9.4 Rare Events, the Sample, Decision and Conclusion
    6. 9.5 Additional Information and Full Hypothesis Test Examples
    7. 9.6 Hypothesis Testing of a Single Mean and Single Proportion
    8. Key Terms
    9. Chapter Review
    10. Formula Review
    11. Practice
    12. Homework
    13. References
    14. Solutions
  11. 10 Hypothesis Testing with Two Samples
    1. Introduction
    2. 10.1 Two Population Means with Unknown Standard Deviations
    3. 10.2 Two Population Means with Known Standard Deviations
    4. 10.3 Comparing Two Independent Population Proportions
    5. 10.4 Matched or Paired Samples
    6. 10.5 Hypothesis Testing for Two Means and Two Proportions
    7. Key Terms
    8. Chapter Review
    9. Formula Review
    10. Practice
    11. Homework
    12. Bringing It Together: Homework
    13. References
    14. Solutions
  12. 11 The Chi-Square Distribution
    1. Introduction
    2. 11.1 Facts About the Chi-Square Distribution
    3. 11.2 Goodness-of-Fit Test
    4. 11.3 Test of Independence
    5. 11.4 Test for Homogeneity
    6. 11.5 Comparison of the Chi-Square Tests
    7. 11.6 Test of a Single Variance
    8. 11.7 Lab 1: Chi-Square Goodness-of-Fit
    9. 11.8 Lab 2: Chi-Square Test of Independence
    10. Key Terms
    11. Chapter Review
    12. Formula Review
    13. Practice
    14. Homework
    15. Bringing It Together: Homework
    16. References
    17. Solutions
  13. 12 Linear Regression and Correlation
    1. Introduction
    2. 12.1 Linear Equations
    3. 12.2 Scatter Plots
    4. 12.3 The Regression Equation
    5. 12.4 Testing the Significance of the Correlation Coefficient
    6. 12.5 Prediction
    7. 12.6 Outliers
    8. 12.7 Regression (Distance from School)
    9. 12.8 Regression (Textbook Cost)
    10. 12.9 Regression (Fuel Efficiency)
    11. Key Terms
    12. Chapter Review
    13. Formula Review
    14. Practice
    15. Homework
    16. Bringing It Together: Homework
    17. References
    18. Solutions
  14. 13 F Distribution and One-Way ANOVA
    1. Introduction
    2. 13.1 One-Way ANOVA
    3. 13.2 The F Distribution and the F-Ratio
    4. 13.3 Facts About the F Distribution
    5. 13.4 Test of Two Variances
    6. 13.5 Lab: One-Way ANOVA
    7. Key Terms
    8. Chapter Review
    9. Formula Review
    10. Practice
    11. Homework
    12. References
    13. Solutions
  15. A | Review Exercises (Ch 3-13)
  16. B | Practice Tests (1-4) and Final Exams
  17. C | Data Sets
  18. D | Group and Partner Projects
  19. E | Solution Sheets
  20. F | Mathematical Phrases, Symbols, and Formulas
  21. G | Notes for the TI-83, 83+, 84, 84+ Calculators
  22. H | Tables
  23. Index
1.
xP(x)
00.12
10.18
20.30
30.15
40.10
50.10
60.05
Table 4.37
3.

0.10 + 0.05 = 0.15

5.

1

7.

0.35 + 0.40 + 0.10 = 0.85

9.

1(0.15) + 2(0.35) + 3(0.40) + 4(0.10) = 0.15 + 0.70 + 1.20 + 0.40 = 2.45

11.
xP(x)
00.03
10.04
20.08
30.85
Table 4.38
13.

Let X = the number of events Javier volunteers for each month.

15.
xP(x)
00.05
10.05
20.10
30.20
40.25
50.35
Table 4.39
17.

1 – 0.05 = 0.95

19.

0.2 + 1.2 + 2.4 + 1.6 = 5.4

21.

The values of P(x) do not sum to one.

23.

Let X = the number of years a physics major will spend doing post-graduate research.

25.

1 – 0.35 – 0.20 – 0.15 – 0.10 – 0.05 = 0.15

27.

1(0.35) + 2(0.20) + 3(0.15) + 4(0.15) + 5(0.10) + 6(0.05) = 0.35 + 0.40 + 0.45 + 0.60 + 0.50 + 0.30 = 2.6 years

29.

X is the number of years a student studies ballet with the teacher.

31.

0.10 + 0.05 + 0.10 = 0.25

33.

The sum of the probabilities sum to one because it is a probability distribution.

35.

2( 40 52 )+30( 12 52 )=1.54+6.92=5.38 2( 40 52 )+30( 12 52 )=1.54+6.92=5.38

37.

X = the number that reply “yes”

39.

0, 1, 2, 3, 4, 5, 6, 7, 8

41.

5.7

43.

0.4151

45.

X = the number of freshmen selected from the study until one replied "yes" that same-sex couples should have the right to legal marital status.

47.

1,2,…

49.

1.4

51.

X = the number of business majors in the sample.

53.

2, 3, 4, 5, 6, 7, 8, 9

55.

6.26

57.

0, 1, 2, 3, 4, …

59.

0.0485

61.

0.0214

63.

X = the number of U.S. teens who die from motor vehicle injuries per day.

65.

0, 1, 2, 3, 4, ...

67.

No

71.

The variable of interest is X, or the gain or loss, in dollars.

The face cards jack, queen, and king. There are (3)(4) = 12 face cards and 52 – 12 = 40 cards that are not face cards.

We first need to construct the probability distribution for X. We use the card and coin events to determine the probability for each outcome, but we use the monetary value of X to determine the expected value.

Card Event X net gain/loss P(X)
Face Card and Heads 6 ( 12 52 )( 1 2 )=( 6 52 ) ( 12 52 )( 1 2 )=( 6 52 )
Face Card and Tails 2 ( 12 52 )( 1 2 )=( 6 52 ) ( 12 52 )( 1 2 )=( 6 52 )
(Not Face Card) and (H or T) –2 ( 40 52 )( 1 )=( 40 52 ) ( 40 52 )( 1 )=( 40 52 )
Table 4.40
  • Expected value=(6)( 6 52 )+(2)( 6 52 )+(2)( 40 52 )= 32 52 Expected value=(6)( 6 52 )+(2)( 6 52 )+(2)( 40 52 )= 32 52
  • Expected value = –$0.62, rounded to the nearest cent
  • If you play this game repeatedly, over a long string of games, you would expect to lose 62 cents per game, on average.
  • You should not play this game to win money because the expected value indicates an expected average loss.
73.
  1. 0.1
  2. 1.6
75.
  1. Software Company
    x P(x)
    5,000,0000.10
    1,000,0000.30
    –1,000,0000.60
    Table 4.41
    Hardware Company
    x P(x)
    3,000,0000.20
    1,000,0000.40
    –1,000,000.40
    Table 4.42
    Biotech Firm
    x P(x)
    6,00,0000.10
    00.70
    –1,000,0000.20
    Table 4.43
  2. $200,000; $600,000; $400,000
  3. third investment because it has the lowest probability of loss
  4. first investment because it has the highest probability of loss
  5. second investment
77.

4.85 years

79.

b

81.

Let X = the amount of money to be won on a ticket. The following table shows the PDF for X.

x P(x)
00.969
5 250 10,000 250 10,000 = 0.025
25 50 10,000 50 10,000 = 0.005
100 10 10,000 10 10,000 = 0.001
Table 4.44

Calculate the expected value of X.

0(0.969) + 5(0.025) + 25(0.005) + 100(0.001) = 0.35

A fair price for a ticket is $0.35. Any price over $0.35 will enable the lottery to raise money.

83.

X = the number of patients calling in claiming to have the flu, who actually have the flu.

X = 0, 1, 2, ...25

85.

0.0165

87.
  1. X = the number of DVDs a Video to Go customer rents
  2. 0.12
  3. 0.11
  4. 0.77
89.

d. 4.43

91.

c

93.
  • X = number of questions answered correctly
  • X ~ B ( 32,  1 3 ) ( 32,  1 3 )
  • We are interested in MORE THAN 75% of 32 questions correct. 75% of 32 is 24. We want to find P(x > 24). The event "more than 24" is the complement of "less than or equal to 24."
  • Using your calculator's distribution menu: 1 – binomcdf ( 32,  1 3 , 24 ) ( 32,  1 3 , 24 )
  • P(x > 24) = 0
  • The probability of getting more than 75% of the 32 questions correct when randomly guessing is very small and practically zero.
95.
  1. X = the number of college and universities that offer online offerings.
  2. 0, 1, 2, …, 13
  3. X ~ B(13, 0.96)
  4. 12.48
  5. 0.0135
  6. P(x = 12) = 0.3186 P(x = 13) = 0.5882 More likely to get 13.
97.
  1. X = the number of fencers who do not use the foil as their main weapon
  2. 0, 1, 2, 3,... 25
  3. X ~ B(25,0.40)
  4. 10
  5. 0.0442
  6. The probability that all 25 not use the foil is almost zero. Therefore, it would be very surprising.
99.
  1. X = the number of audits in a 20-year period
  2. 0, 1, 2, …, 20
  3. X ~ B(20, 0.02)
  4. 0.4
  5. 0.6676
  6. 0.0071
101.
  1. X = the number of matches
  2. 0, 1, 2, 3
  3. X ~ B ( 3, 1 6 ) ( 3, 1 6 )
  4. In dollars: −1, 1, 2, 3
  5. 1 2 1 2
  6. Multiply each Y value by the corresponding X probability from the PDF table. The answer is −0.0787. You lose about eight cents, on average, per game.
  7. The house has the advantage.
103.
  1. X ~ B(15, 0.281)
    This histogram shows a binomial probability distribution. It is made up of bars that are fairly normally distributed. The x-axis shows values from 0 to 15, with bars from 0 to 9. The y-axis shows values from 0 to 0.25 in increments of 0.05.
    Figure 4.10
    1. Mean = μ = np = 15(0.281) = 4.215
    2. Standard Deviation = σ = npq npq = 15(0.281)(0.719) 15(0.281)(0.719) = 1.7409
  2. P(x > 5) = 1 – P(x ≤ 5) = 1 – binomcdf(15, 0.281, 5) = 1 – 0.7754 = 0.2246
    P(x = 3) = binompdf(15, 0.281, 3) = 0.1927
    P(x = 4) = binompdf(15, 0.281, 4) = 0.2259
    It is more likely that four people are literate that three people are.
105.
  1. X = the number of adults in America who are surveyed until one says he or she will watch the Super Bowl.
  2. X ~ G(0.40)
  3. 2.5
  4. 0.0187
  5. 0.2304
107.


  1. X = the number of pages that advertise footwear
  2. X takes on the values 0, 1, 2, ..., 20
  3. X ~ B(20, 2919229192)
  4. 3.02
  5. No
  6. 0.9997
  7. X = the number of pages we must survey until we find one that advertises footwear. X ~ G(2919229192)
  8. 0.3881
  9. 6.6207 pages
109.

0, 1, 2, and 3

111.
  1. X ~ G(0.25)
    1. Mean = μ = 1 p 1 p = 1 0.25 1 0.25 = 4
    2. Standard Deviation = σ = 1p p 2 1p p 2 = 10.25 0.25 2 10.25 0.25 2 ≈ 3.4641
  2. P(x = 10) = geometpdf(0.25, 10) = 0.0188
  3. P(x = 20) = geometpdf(0.25, 20) = 0.0011
  4. P(x ≤ 5) = geometcdf(0.25, 5) = 0.7627
113.
  1. X = the number of pages that advertise footwear
  2. 0, 1, 2, 3, ..., 20
  3. X ~ H(29, 163, 20); r = 29, b = 163, n = 20
  4. 3.03
  5. 1.5197
115.
  1. X = the number of Patriots picked
  2. 0, 1, 2, 3, 4
  3. X ~ H(4, 8, 9)
  4. Without replacement
117.
  1. X ~ P(5.5); μ = 5.5; σ =  5.5 σ =  5.5 ≈ 2.3452
  2. P(x ≤ 6) = poissoncdf(5.5, 6) ≈ 0.6860
  3. There is a 15.7% probability that the law staff will receive more calls than they can handle.
  4. P(x > 8) = 1 – P(x ≤ 8) = 1 – poissoncdf(5.5, 8) ≈ 1 – 0.8944 = 0.1056
119.

Let X = the number of defective bulbs in a string.

Using the Poisson distribution:

  • μ = np = 100(0.03) = 3
  • X ~ P(3)
  • P(x ≤ 4) = poissoncdf(3, 4) ≈ 0.8153

Using the binomial distribution:

  • X ~ B(100, 0.03)
  • P(x ≤ 4) = binomcdf(100, 0.03, 4) ≈ 0.8179

The Poisson approximation is very good—the difference between the probabilities is only 0.0026.

121.
  1. X = the number of children for a Spanish woman
  2. 0, 1, 2, 3,...
  3. X ~ P(1.47)
  4. 0.2299
  5. 0.5679
  6. 0.4321
123.
  1. X = the number of fortune cookies that have an extra fortune
  2. 0, 1, 2, 3,... 144
  3. X ~ B(144, 0.03) or P(4.32)
  4. 4.32
  5. 0.0124 or 0.0133
  6. 0.6300 or 0.6264
  7. As n gets larger, the probabilities get closer together.
125.
  1. X = the number of people audited in one year
  2. 0, 1, 2, ..., 100
  3. X ~ P(2)
  4. 2
  5. 0.1353
  6. 0.3233
127.
  1. X = the number of shell pieces in one cake
  2. 0, 1, 2, 3,...
  3. X ~ P(1.5)
  4. 1.5
  5. 0.2231
  6. 0.0001
  7. Yes
129.

d

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