Statistics A Tool for Social Research International Edition 9th Edition by Joseph F. Healey – Test Bank

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Sample Questions Posted Below

 

Chapter 5

THE NORMAL CURVE

Multiple Choice Questions

1. A defining characteristic of the normal curve is that it is

a. theoretical

b. positively skewed

c. negatively skewed

d. perfectly nonsymmetrical

Answer: a Page: 118 LO: 1

2. By definition, the normal curve is

a. symmetrical

b. positively skewed

c. negatively skewed

d. empirical

Answer: a Page: 118 LO: 1

3. a. b. c. d. The tails of the theoretical normal curve

intersect with the horizontal axis between the 4th and 5th standard deviation

intersect with the horizontal axis beyond the 5th standard deviation

never touch the horizontal axis

maintain the same distance above the horizontal axis beyond the 3rd

standard deviation

Answer: c Page: 118 LO: 1

4. Unlike empirical distribution, the theoretical normal curve is

a. positively skewed

b. negatively skewed

c. bimodal

d. perfectly symmetrical

Answer: d Page: 118 LO: 1

5. will be

a. b. c. d. On all normal curves the area between the mean and ± 1 standard deviation

about 34% of the total area

about 68% of the total area

50% of the total area

99.9% of the total area

Answer: b Page: 120 LO: 1

6. will be

a. b. c. d. On all normal curves the area between the mean and ± 2 standard deviations

about 34% of the total area

about 95% of the total area

less than 50% of the total area

about 68% of the total area

Answer: b Page: 120 LO: 17.On all normal curves the area between the mean and +1 standard deviation will be

a. b. c. d. about 34% of the total area

about 68% of the total area

about 95% of the total area

about 99% of the total area

Answer: a Page: 120 LO: 1

8. Assuming a normal distribution of 1000 cases, how many cases will be farther

away from the mean than + 3 standard deviations?

a. at least 500

b. about 3

c. 327

d. it’s impossible to estimate

Answer: b Page: 121 LO: 2

9. Assuming a normal distribution of 1000 cases, how many cases will be within

± 1 standard deviations of the mean?

a. at least 500

b. about 3

c. about 680

d. it’s impossible to estimate

Answer: c Page: 121 LO: 2

10. As the standard deviation of a normal distribution increases, the percentage

of the area between ± 1 standard deviation will

a. increase

b. stay the same

c. decrease

d. become non-symmetrical

Answer: b Page: 120 LO: 1

11. The area beyond ± 2 standard deviations contains approximately what % of

the area under the normal curve?

a. 75%

b. 50%

c. 99%

d. 5%

Answer: d Page: 120 LO: 2

12. a. b. c. d. Distributions of IQ scores are normally distributed because

the underlying quality being tested – intelligence – is normally distributed

IQ tests are designed to produce in normal distributions

there is no cultural bias in the tests

they reflect the natural distribution of intelligence: human beings are

genetically programmed to have an average intelligence of about 100.

Answer: b Page: 121 LO: 1

13.Converting scores into Z scores standardizes the original distribution to units of the

a. median

b. standard deviation

c. mean

d. percentage

Answer: b Page: 122 LO: 2

14. a. b. c. d. A Z score of +1.00 indicates a score that lies

one standard deviation unit to the right of the mean

one standard deviation unit to the left of the mean

1/2 of one standard deviation unit on each side of the mean

any of the above are possible

Answer: a Page: 122 LO: 2

15. a. b. c. d. A Z score of -2.00 indicates a score that lies

two standard deviation units to the right of the mean

two standard deviation units to the left of the mean

0.5 of one standard deviation unit on each side of the mean

any of the above are possible depending on the value of the mean

Answer: b Page: 122 LO: 2

16. The standardized normal distribution (or Z distribution) has

a. a mean of 0 and a standard deviation of 1

b. a mean of 1 and a standard deviation of 0

c. a mean equal to the average of the scores and a standard deviation equal to

the mean

d. a mean of 1 and a standard deviation of 1

Answer: a Page: 122 LO: 2

17. a. b. c. When an empirical normal distribution of scores is standardized

the mean will become 0

the standard deviation will become 1

each score will be converted to a Z score

d. all of the above

Answer: d Page: 122 LO: 2

18. If a Z score is 0, then the value of the corresponding raw score would be

a. 0

b. the same as the mean of the empirical distribution

c. the same as the standard deviation of the empirical distribution

d. probably a negative number

Answer: b Page: 122 LO: 2

19. a. 0

b. c. If a Z score is + 1.00, then the value of the corresponding raw score would be

the same as the mean of the empirical distribution

equal to the mean of the empirical distribution plus one standard deviation

d. probably a negative number

Answer: c Page: 122 LO: 220.The Z score table gives the area between a score and the mean. For a Z score of –

1.00 that area (in percentages) is

a. 34.13%

b. -34.13%

c. 68.26%

d. -68.26%

Answer: a Page: 122 LO: 2

21. a. b. c. d. Column c in the normal curve table lists “areas beyond Z”. below a positive Z score

above a negative Z score

between two positive Z scores

above a positive Z score

Answer: d Page: 121 LO: 22

This is the area

22. The area between the mean and a Z score of +1.50 is 43.32%. This score is

higher than _________ of the scores in the distribution.

a. 43.32%

b. 51.50%

c. 57.68%

d. 93.32%

Answer: d Page: 122-124 LO: 2

23. The area between the mean and a Z score of +1.50 is 43.32%. This score is

less than _________ of the scores in the distribution.

a. 43.32%

b. 6.68%

c. 3.32%

d. 93.32%

Answer: b Page: 122-124 LO: 2

24. The mean score on a final chemistry exam was 75, and the standard

deviation of the scores was 5. If the distribution is normal and your score was 70,

what percentage of the scores was lower than yours?

a. 15.87%

b. 30.00%

c. 34.13%

d. 50.00%

Answer: a Page: 122-124 LO: 2

25. The mean on a standardized test is 100 and the standard deviation is 35. Your

score is 65. What percentage of the scores were higher than yours?

a. about 84%

b. no more than 50%

c. about 34%

d. about 16%

Answer: a Page: 122-124 LO: 2

26.To find the area above a positive Z score or below a negative Z score you would

a. b. c. d. subtract the value of the Z score from the mean

use the “Area Beyond Z” column of the Z score table

add the value of the Z score to the area beyond the mean

add the area between the Z score and the mean to 100%

Answer: b Page: 124-126 LO: 2

27. would

a. b. 50%

c. d. To obtain the area below a positive Z score or above a negative Z score you

subtract the value of the Z score from the mean

subtract the area in the “Area Beyond Z” column of the Z score table from

add the value of the Z score to the area beyond the mean

add the area between the Z score and the mean to 50%

Answer: d Page: 124-126 LO: 2

28. The Z scores of two tests scores are + 1.2 and + 1.5. To obtain the area

between these scores

a. subtract the Z scores and find the area of the difference in the Z score table

b. find the area between each score and the mean in the Z score table and then

subtract the smaller area from the larger area

c. find the area between each score and the mean in the Z score table and then

subtract the

difference between them from 100%

d. find the area beyond each score in the Z score table and subtract the

difference between the areas from the mean

Answer: b Page: 127-129 LO: 2

29. The area between a negative Z score and a positive Z score can be found by

a. subtracting the Z scores from each other

b. subtracting each Z score from the mean and adding the results

c. adding the Z scores and finding the area in the Z score table for the summed

Z scores

d. adding the areas between each Z score and the mean

Answer: d Page: 127-129 LO: 2

30. a. b. c. d. The Z scores of two test scores are – 1.17 and + 2.38. To find the total area

between these two scores

add the column b areas together

subtract each score from the mean and divide the result by the standard

deviation

add the column b area to the column c area

add the column c areas

Answer: d Page: 127-129 LO: 2

31. a. b. c. The area between two negative Z scores can be found by

adding the Z scores and finding the area below the total Z score

subtracting the Z scores and finding the total area above the total Z score

finding the area between each Z score and the mean and subtracting the

smaller area from the largerd. 32.

finding the area between each Z score and the mean and adding the areas

Answer: c Page: 127-129 LO: 2To estimate probabilities, set up a fraction with the number of _________ in the

numerator and the number of _________ in the denominator

a. successes, failures

b. possible outcomes, successes

c. failures, successes

d. successes, possible outcomes

Answer: d Page: 130 LO: 3

33. The probability of getting a 1 in a single toss of a six sided die would be

a. 2 to 1

b. 60 to 1

c. 1 in 6

d. impossible to estimate with the information given

Answer: c Page: 130 LO: 3

34. As used in the social sciences, probabilities are a type of ___________ which

can vary from _____________ .

a. percentage, 0 to 1

b. fraction, 0 to 100

c. proportion, 0.00 to 1.00

d. Z score, 0 to infinity

Answer: c Page: 130 LO: 3

35. a. b. c. d. If a case is randomly selected from a normal distribution, the score of the

case will most likely be

equal to the mean in value

close to the mean in value

at least 1 standard deviation above the mean

at least 1 standard deviation below the mean

Answer: b Page: 131 LO: 3

36. The probability that a randomly selected case will have a score beyond ±

1.00 standard deviation of the mean is

a. 0.6826

b. 0.5000

c. 0.3174

d. 1/2 of the area of 1 standard deviation

Answer: c Page: 131 LO: 3

37. A social researcher has constructed a measure of racial prejudice and

obtained a distribution of scores on this measure from a randomly selected sample

of public office holders. The scores were normally distributed with a mean of 45

and a standard deviation of 7. What is the probability that a randomly selected

case from the sample will have a score less than 38?

a. 0.4526

b. 0.5018

c. 0.5200

d. 0.1587

Answer: d Page: 132 LO: 338.What is the probability that a randomly selected case from the sample in the

previous question would have a score of 52 or more?

a. 0.7500

b. 0.6826

c. 0.3413

d. 0.1587

Answer: d Page: 132 LO: 3

39. What is the probability that a randomly selected case from a normally

distributed distribution will have a score between -1.00 and the mean?

a. 0.34

b. 0.16

c. 0.50

d. 0.86

Answer: a Page: 132 LO: 3

40. The average homicide rate for the cities and towns in a state is 10 per

100,000 population with a standard deviation of 2. If the variable is normally

distributed, what is the probability that a randomly selected town will have a

homicide rate greater than 14?

a. 0.34

b. 0.68

c. 0.50

d. 0.02

Answer: d Page: 132 LO: 3

41. The average homicide rate for the cities and towns in a state is 10 per

100,000 population with a standard deviation of 2. If the variable is normally

distributed, what is the probability that a randomly selected town will have a

homicide rate greater than 8?

a. 0.34

b. 0.68

c. 0.84

d. 0.01

Answer: c Page: 132 LO: 3

42. The text discusses an application of probability theory that involved

a. betting on horse races

b. casino gambling

c. cheating on final exams

d. betting on the outcome of the presidential election

Answer: b Page: 132 LO: 3Problems

1. A sample of university students has an average GPA of 2.78 with a standard

deviation of 0.45. If GPA is normally distributed, what percentage of the students

has GPAs

Z score Area

a. less than 2.30

b. less than 2.00

c. more than 2.00

d. more than 3.00

e. between 2.50

and 3.50

f. between 2.00

and 2.50

2. For the distribution of GPAs described in problem 1, what is the probability that

a randomly selected student will have a GPA

Z score Probability

a. less than 3.40

b. less than 3.78

c. more than 3.50

d. more than 2.50

e. between 2.00

and 3.00

f. between 3.00

and 3.50Answers to Problems

1.

Z score Area

a.

-1.07

14.23%

b.

-1.73

4.18%

c.

-1.73

95.82%

d.

0.49

31.21%

e.

-0.62 and 1.60

67.76%

f.

-1.73 and -0.62

22.58%

2.

Z score Area

a. 1.38 0.92

b. 2.22 0.99

c. 1.60 0.06

d. -0.62 0.73

e. -1.73 and 0.49 0.65

f. 0.49 and 1.60 0.26