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1. Find the odds against correctly...

1. Find the odds against correctly guessing the answer to a multiple-choice question with 4 possible answers.

2. The distribution of B.A. degrees conferred by a local college is listed below (by major):

Major Frequency

English 2073

Mathematics 2164

Chemistry 318

Physics 856

Liberal Arts 1358

Business 1676

Engineering 868

9313

What is the probability that a randomly selected degree is NOT in Engineering? Please round to the nearest ten thousandth, if necessary.

3. A sample of 100 wood and 100 graphite tennis rackets is taken from the warehouse. If 25 wood and 20 graphite rackets are defective and one racket is randomly selected from the sample, find the probability that the racket is wood or defective.

4. The table below describes the smoking habits of a group of asthma sufferers.

Nonsmoker Occasional Smoker Regular Smoker Heavy Smoker Total

Men 384 19 72 36 511

Women 322 46 77 44 489

Total 706 65NNN-NN-NNNN

If one of the 1000 people is randomly selected, find the probability of getting someone who is a regular or heavy smoker.

5. A batch consists of 15 defective coils and 85 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made

6. The test scores of 45 students are summarized in the frequency table below. Find the mean score.

Score Students

50-59 14

60-69 11

70-79 5

80-89 9

90-99 6

Find the mode(s) for the given sample data.

7. 7.29, 7.41, 7.56, 7.88, 7.99, 7.62

In 8 and 9, identify the given random variable as being discrete or continuous.

8. The number of votes cast for H. Ross Perot in the 1992 election.

9. The average speed of cars passing a busy intersection between 4:30 P.M. and 6:30 P.M. on a Friday is 32.3 mi/h.

10. The frequency table below shows the distribution of students' scores on an exam. Construct the relative frequency table.

Score Frequency

91-100 3

81-90 9

71-80 6

61-70 6

<61 5

11. Find the standard deviation for the given probability distribution.

x P(x)

0 0.19

1 0.28

2 0.14

3 0.26

4 0.13

12. The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.6274, 0.3102, 0.0575, 0.0047, and 0.0001, respectively. Find the standard deviation for the probability distribution.

13. The data set represents the income levels of the members of a country club. Using the relative frequency approach, estimate the probability that a randomly selected member earns at least $100,000.

108,000 124,000 90,000 132,000 91,000 108,000 92,000 88,000 148,000 188,000 89,000 100,000 140,000 91,000 124,000 116,000 92,000 156,000 87,000 116,000

14. The frequency table describes the distribution of birds viewed by a bird watching group.

Bird frequency

Wren 4

Crow 7

Hawk 2

Goose 13

Cardinal 4

Estimate the probability that the group will see a Cardinal on the next bird watching trip. Round your answer to thousandths.

For 15 and 16, determine whether they each represent probability distributions. If not, identify the requirement that is not satisfied.

15.

x P(x)

0 0.148

1 0.226

2 0.211

3 0.144

4 0.163

5 0.225

16. A police department reports that the probabilities that 0, 1, 2, 3, and 4 car thefts will be reported in a given day are 0.122, 0.257, 0.270, 0.189, and 0.162, respectively.

Identify the abuse of statistics in 17 and 18.

17. "38% of adults in the United States regularly visit a doctor". A college student reached this conclusion after she had questioned 520 randomly selected members of her college. What is wrong with her survey?

18. A company accused of downsizing workers by shipping job overseas defended itself with the following statement "Yes, we were forced to lay off 20% of our workforce last year, but this year we increased our workforce by 20% and we therefore now have the same number of employees as before the layoff." What is the flaw in this argument?

19. One purpose of displaying data graphically is to provide clues about trends. The given values are weights (ounces) of steaks listed on a restaurant menu as "20 ounce porterhouse" steaks. The weights are supposed to be 21 ounces because they supposedly lose an ounce when cooked. Create a frequency distribution with 5 classes. Based on your distribution, comment on the advertised “20-ounce" steaks.

17 20 21 18 20 20 20 18 19 19 20 19 21 20 18 20 20 19 18 19

20. Kevin asked some of his friends how many hours they had worked during the previous week at their after-school jobs. The results are shown below.

6 5 6 3 6 6 9 8 6 4 8 5

5 8 6 5 8 6 5 8 5 8 8 3

Construct a frequency table. Use 4 classes, a class width of 2 hours, and a lower limit of 3 for class 1.

2. The distribution of B.A. degrees conferred by a local college is listed below (by major):

Major Frequency

English 2073

Mathematics 2164

Chemistry 318

Physics 856

Liberal Arts 1358

Business 1676

Engineering 868

9313

What is the probability that a randomly selected degree is NOT in Engineering? Please round to the nearest ten thousandth, if necessary.

3. A sample of 100 wood and 100 graphite tennis rackets is taken from the warehouse. If 25 wood and 20 graphite rackets are defective and one racket is randomly selected from the sample, find the probability that the racket is wood or defective.

4. The table below describes the smoking habits of a group of asthma sufferers.

Nonsmoker Occasional Smoker Regular Smoker Heavy Smoker Total

Men 384 19 72 36 511

Women 322 46 77 44 489

Total 706 65NNN-NN-NNNN

If one of the 1000 people is randomly selected, find the probability of getting someone who is a regular or heavy smoker.

5. A batch consists of 15 defective coils and 85 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made

6. The test scores of 45 students are summarized in the frequency table below. Find the mean score.

Score Students

50-59 14

60-69 11

70-79 5

80-89 9

90-99 6

Find the mode(s) for the given sample data.

7. 7.29, 7.41, 7.56, 7.88, 7.99, 7.62

In 8 and 9, identify the given random variable as being discrete or continuous.

8. The number of votes cast for H. Ross Perot in the 1992 election.

9. The average speed of cars passing a busy intersection between 4:30 P.M. and 6:30 P.M. on a Friday is 32.3 mi/h.

10. The frequency table below shows the distribution of students' scores on an exam. Construct the relative frequency table.

Score Frequency

91-100 3

81-90 9

71-80 6

61-70 6

<61 5

11. Find the standard deviation for the given probability distribution.

x P(x)

0 0.19

1 0.28

2 0.14

3 0.26

4 0.13

12. The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.6274, 0.3102, 0.0575, 0.0047, and 0.0001, respectively. Find the standard deviation for the probability distribution.

13. The data set represents the income levels of the members of a country club. Using the relative frequency approach, estimate the probability that a randomly selected member earns at least $100,000.

108,000 124,000 90,000 132,000 91,000 108,000 92,000 88,000 148,000 188,000 89,000 100,000 140,000 91,000 124,000 116,000 92,000 156,000 87,000 116,000

14. The frequency table describes the distribution of birds viewed by a bird watching group.

Bird frequency

Wren 4

Crow 7

Hawk 2

Goose 13

Cardinal 4

Estimate the probability that the group will see a Cardinal on the next bird watching trip. Round your answer to thousandths.

For 15 and 16, determine whether they each represent probability distributions. If not, identify the requirement that is not satisfied.

15.

x P(x)

0 0.148

1 0.226

2 0.211

3 0.144

4 0.163

5 0.225

16. A police department reports that the probabilities that 0, 1, 2, 3, and 4 car thefts will be reported in a given day are 0.122, 0.257, 0.270, 0.189, and 0.162, respectively.

Identify the abuse of statistics in 17 and 18.

17. "38% of adults in the United States regularly visit a doctor". A college student reached this conclusion after she had questioned 520 randomly selected members of her college. What is wrong with her survey?

18. A company accused of downsizing workers by shipping job overseas defended itself with the following statement "Yes, we were forced to lay off 20% of our workforce last year, but this year we increased our workforce by 20% and we therefore now have the same number of employees as before the layoff." What is the flaw in this argument?

19. One purpose of displaying data graphically is to provide clues about trends. The given values are weights (ounces) of steaks listed on a restaurant menu as "20 ounce porterhouse" steaks. The weights are supposed to be 21 ounces because they supposedly lose an ounce when cooked. Create a frequency distribution with 5 classes. Based on your distribution, comment on the advertised “20-ounce" steaks.

17 20 21 18 20 20 20 18 19 19 20 19 21 20 18 20 20 19 18 19

20. Kevin asked some of his friends how many hours they had worked during the previous week at their after-school jobs. The results are shown below.

6 5 6 3 6 6 9 8 6 4 8 5

5 8 6 5 8 6 5 8 5 8 8 3

Construct a frequency table. Use 4 classes, a class width of 2 hours, and a lower limit of 3 for class 1.

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