Social Statistics For A Diverse Society 8th Edition By Frankfort Nachmias – Test Bank

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Chapter 5: The Normal Distribution

Test Bank

Multiple Choice

 

  1. The normal distribution is a ______ and ______ symmetrical distribution with the mean, the median, and the mode all coinciding at its peak and with the frequencies gradually decreasing at both ends of the curve.
  2. bell-shaped; empirical
  3. bell-shaped; theoretical
  4. curvilinear; hypothetical
  5. curvilinear; inferential

Ans: b

Learning Objective: 5-2: Describe the properties of the normal distribution

Cognitive Domain: Knowledge

Answer Location: Properties of the Normal Distribution

Difficulty Level: Easy

 

  1. Considering the properties of the normal curve, if we know the mean and standard deviation, we are then able to calculate the ______ under the curve between any score and the mean.
  2. range
  3. area
  4. mean
  5. mode

Ans: b

Learning Objective: 5-2: Describe the properties of the normal distribution

Cognitive Domain: Knowledge

Answer Location: Areas Under the Normal Curve

Difficulty Level: Medium

 

  1. What percentage of the area under the normal curve falls between ±2 standard deviations?
  2. 99.72
  3. 95.46
  4. 68.26
  5. 20.0

Ans: b

Learning Objective: 5-2: Describe the properties of the normal distribution

Cognitive Domain: Knowledge

Answer Location: Areas Under the Normal Curve

Difficulty Level: Easy

 

  1. The number of standard deviations that a given raw score is above or below the mean is referred to as a
  2. mean.
  3. frequency distribution.
  4. variance.
  5. standard (Z) score.

Ans: d

Learning Objective: 5-3: Transform a raw score into standard (Z) score and vice versa

Cognitive Domain: Knowledge

Answer Location: Transforming a Raw Score Into a Z Score

Difficulty Level: Easy

 

  1. Suppose that in a particular sample, the mean is 70.07 and the standard deviation is 10.27. What is the Z score that corresponds to a raw score of 80?
  2. 0.97
  3. 6.82
  4. 9.93
  5. 14.61

Ans: a

Learning Objective: 5-3: Transform a raw score into standard (Z) score and vice versa

Cognitive Domain: Application

Answer Location: Transforming a Raw Score into a Z Score

Difficulty Level: Easy

 

  1. Suppose that in a particular sample, the mean is 70.07 and the standard deviation is 10.27. What is the raw score associated with a Z score of 1.88?
  2. 80.54
  3. 88.00
  4. 89.38
  5. 90.27

Ans: c

Learning Objective: 5-3: Transform a raw score into standard (Z) score and vice versa

Cognitive Domain: Application

Answer Location: Transforming a Raw Score into a Z Score

Difficulty Level: Easy

 

  1. A normal distribution represented in Z scores is referred to as a:
  2. normal distribution.
  3. normal bell-curve.
  4. standard normal distribution.
  5. standard normal table.

Ans: c

Learning Objective: 5-1: Explain the importance and use of the normal distribution in statistics

Cognitive Domain: Knowledge

Answer Location: The Standard Normal Distribution

Difficulty Level: Easy

 

  1. A standard normal table shows the area under the standard normal curve corresponding to any ______ or its fraction.
  2. bell-curve
  3. Z score
  4. raw score
  5. standard deviation

Ans: b

Learning Objective: 5-1: Explain the importance and use of the normal distribution in statistics

Cognitive Domain: Knowledge

Answer Location: The Standard Normal Distribution

Difficulty Level: Medium

 

  1. For a Z score of zero, what is the proportion of area between the mean and the Z score?
  2. 0.0
  3. .05
  4. .50
  5. 1.0

Ans: a

Learning Objective: 5-1: Explain the importance and use of the normal distribution in statistics

Cognitive Domain: Comprehension

Answer Location: The Standard Normal Distribution

Difficulty Level: Easy

 

  1. For a Z score of zero, what is the proportion of area beyond the Z score?
  2. 0.0
  3. .05
  4. .50
  5. 1.0

Ans: c

Learning Objective: 5-2: Describe the properties of the normal distribution

Cognitive Domain: Comprehension

Answer Location: The Standard Normal Table

Difficulty Level: Medium

 

  1. To find proportion of the area under the normal curve between two Z scores that are both above the mean, it is necessary to examine the
  2. quotient obtained by dividing the larger Z score by the smaller.
  3. product obtained by multiplying the smaller Z score by the larger Z score.
  4. difference between the areas beyond each Z score.
  5. sum of the areas associated with each Z score.

Ans: c

Learning Objective: 5-4: Transform a Z score into proportion (or percentage) and vice versa

Cognitive Domain: Analysis

Answer Location: Finding the Area Between the Mean and a Positive or Negative Z Score

Difficulty Level: Medium

 

  1. To find proportion of the area under the normal curve between two Z scores, one below the mean and the other above the mean, it is necessary to examine the
  2. sum of the areas between each Z score and the mean.
  3. difference of the areas between each Z score and the mean.
  4. sum of the areas beyond each Z score and the mean.
  5. difference of the areas beyond each Z score and the mean.

Ans: a

Learning Objective: 5-4: Transform a Z score into proportion (or percentage) and vice versa

Cognitive Domain: Analysis

Answer Location: Finding the Area Between the Mean and a Positive or Negative Z Score

Difficulty Level: Medium

 

  1. To find the percentile rank of a given score, it is necessary to determine the area
  2. between the mean and the Z score.
  3. below the Z score.
  4. above the Z score.
  5. equal to the mean.

Ans: c

Learning Objective: 5-5: Calculate and interpret the percentile rank of a score

Cognitive Domain: Comprehension

Answer Location: Working with Percentiles in a Normal Distribution

Difficulty Level: Medium

 

  1. Suppose that in a particular sample, the mean is 70.07 and the standard deviation is 10.27. What is the Z score for a raw score of 65?
  2. –0.49
  3. 0.49
  4. –0.51
  5. 0.51

Ans: a

Learning Objective: 5-3: Transform a raw score into standard (Z) score and vice versa

Cognitive Domain: Application

Answer Location: Transforming a Raw Score into a Z Score

Difficulty Level: Easy

 

  1. Suppose that the area above some Z score is 0.31, which when multiplied by 100 equals 31%. What is the term for this quantity?
  2. The mean
  3. The standard deviation
  4. The proportion between the mean and the Z score
  5. The percentile rank

Ans: d

Learning Objective: 5-5: Calculate and interpret the percentile rank of a score

Cognitive Domain: Knowledge

Answer Location: Working with Percentiles in a Normal Distribution

Difficulty Level: Easy

 

  1. What percentage of the area under the normal curve falls between ±1 standard deviations?
  2. 99.72
  3. 95.46
  4. 68.26
  5. 20.00

Ans: c

Learning Objective: 5-2: Describe the properties of the normal distribution

Cognitive Domain: Knowledge

Answer Location: Areas under the Normal Curve

Difficulty Level: Easy

 

  1. What percentage of the area under the normal curve falls between ±3 standard deviations?
  2. 99.72
  3. 95.46
  4. 68.26
  5. 20.00

Ans: a

Learning Objective: 5-2: Describe the properties of the normal distribution

Cognitive Domain: Knowledge

Answer Location: Areas Under the Normal Curve

Difficulty Level: Easy

 

  1. Suppose that in a particular sample, the mean is 50 and the standard deviation is 10. What is the Z score associated with a raw score of 68?
  2. 1.8
  3. 2
  4. –1.8
  5. 11.8

Ans: a

Learning Objective: 5-3: Transform a raw score into standard (Z) score and vice versa

Cognitive Domain: Application

Answer Location: Transforming a Raw Score into a Z Score

Difficulty Level: Easy

 

  1. The normal distribution is central to the theory of ______ statistics.
  2. inferential
  3. descriptive
  4. standardized
  5. biserial

Ans: a

Learning Objective: 5-1: Explain the importance and use of the normal distribution in statistics

Cognitive Domain: Comprehension

Answer Location: Main Points

Difficulty Level: Medium

 

  1. A normal distribution represented in standard Z scores, with
  2. mean = 0 and standard deviation = 1.
  3. mean = 1 and standard deviation = 0.
  4. mean = 0 and standard deviation = 0.
  5. mean = 1 and standard deviation = 1.

Ans: a

Learning Objective: 5-2: Describe the properties of the normal distribution

Cognitive Domain: Knowledge

Answer Location: The Standard Normal Distribution

Difficulty Level: Easy

 

  1. In a normal distribution, there is a constant proportion of the area under the curve lying between the mean and any given distance from the mean and is measured in
  2. variance units.
  3. Z score units.
  4. raw score units.
  5. standard deviation units.

Ans: d

Learning Objective: 5-2: Describe the properties of the normal distribution

Cognitive Domain: Knowledge

Answer Location: Areas Under the Normal Curve

Difficulty Level: Easy

 

 

Multiple Response

 

  1. SELECT ALL THAT APPLY. The normal distribution is
  2. right skew symmetric.
  3. left skew symmetric.
  4. symmetric.
  5. bell-shaped.

Ans: c, d

Learning Objective: 5-2: Describe the properties of the normal distribution

Cognitive Domain: Knowledge

Answer Location: Properties of the Normal Distribution

Difficulty Level: Easy

 

  1. SELECT ALL THAT APPLY. Which of the following coincide in a normal distribution?
  2. mean
  3. median
  4. variance
  5. mode

Ans: a, b, d

Learning Objective: 5-2: Describe the properties of the normal distribution

Cognitive Domain: Knowledge

Answer Location: Properties of the Normal Distribution

Difficulty Level: Easy

 

  1. SELECT ALL THAT APPLY. The area under the normal curve is
  2. 68.28% between the mean and ±2 standard deviation.
  3. equal to 1.00 or 100% of the total observations.
  4. divided into two equal parts by a vertical line through the mean.
  5. a proportion or percentage of the number of observations.

Ans: b, c, d

Learning Objective: 5-2: Describe the properties of the normal distribution

Cognitive Domain: Comprehension

Answer Location: Area Under the Normal Curve

Difficulty Level: Easy

 

 

True/False

 

  1. The normal distribution is a theoretical distribution.

Ans: T

Learning Objective: 5-1: Explain the importance and use of the normal distribution in statistics

Cognitive Domain: Comprehension

Answer Location: The Normal Distribution

Difficulty Level: Easy

 

  1. Scores for an exam are normally distributed with a mean of 235 and a standard deviation of 52. Then the score which corresponds to the bottom 24% is 199 or lower.

Ans: T

Learning Objective: 5-4: Transform a Z score into proportion (or percentage) and vice versa

Cognitive Domain: Application

Answer Location: Finding the Area Above a Positive Z Score or Below a Negative Score

Difficulty Level: Medium

 

  1. Scores for an exam are normally distributed with a mean of 235 and a standard deviation of 52. Then the cut-off point for the top 30% is 270.

Ans: F

Learning Objective: 5-4: Transform a Z score into proportion (or percentage) and vice versa

Cognitive Domain: Application

Answer Location: Finding the Area Above a Positive Z Score or Below a Negative Score

Difficulty Level: Medium

 

  1. Probability can be calculated as: Number of times an event will occur/Total number of events.

Ans: T

Learning Objective: 5-2: Describe the properties of the normal distribution

Cognitive Domain: Knowledge

Answer Location: A Closer Look 5.1—Percentages, Proportions and Probabilities

Difficulty Level: Easy

 

  1. Rare events, with smaller corresponding probabilities, are towards the middle of the normal curve.

Ans: F

Learning Objective: 5-2: Describe the properties of the normal distribution

Cognitive Domain: Comprehension

Answer Location: A Closer Look 5.1—Percentages, Proportions and Probabilities

Difficulty Level: Easy

 

 

Short Answer

 

  1. The mean age at first marriage for respondents in a survey is 23.33, with a standard deviation of 6.13. Calculate the Z score associated with an observed age at first marriage of 25.50.

Ans: 0.35

Learning Objective: 5-3: Transform a raw score into standard (Z) score and vice versa

Cognitive Domain: Application

Answer Location: Transforming a Raw Score into a Z Score

Difficulty Level: Easy

 

  1. The mean age at first marriage for respondents in a survey is 23.33, with a standard deviation of 6.13. Calculate the Z score associated with an observed age at first marriage of 25.50 and provide a substantive interpretation of this quantity.

Ans: 0.35 standard deviation above the mean

Learning Objective: 5-3: Transform a raw score into standard (Z) score and vice versa

Cognitive Domain: Analysis

Answer Location: Transforming a Raw Score into a Z Score

Difficulty Level: Medium

 

  1. The mean age at first marriage for respondents in a survey is 23.33, with a standard deviation of 6.13. The Z score associated with a particular age at first marriage is 0.35. If the proportion of the area between this particular age at first marriage and the mean is 0.14, what proportion of respondents experienced their first marriage earlier than this age?

Ans: 0.50 + 0.14 = 0.64

Learning Objective: 5-2: Describe the properties of the normal distribution | 5-3: Transform a raw score into standard (Z) score and vice versa

Cognitive Domain: Comprehension

Answer Location: The Standard Normal Table; Transforming a Raw Score into a Z Score

Difficulty Level: Medium

 

  1. The mean age at first marriage for respondents in a survey is 23.33, with a standard deviation of 6.13. Calculate the observed age at first marriage associated with a Z score of –0.72.

Ans: 18.91

Learning Objective: 5-3: Transform a raw score into standard (Z) score and vice versa

Cognitive Domain: Application

Answer Location: Transforming a Raw Score into a Z Score

Difficulty Level: Easy

 

  1. The mean age at first marriage for respondents in a survey is 23.33, with a standard deviation of 6.13. Suppose that a person experienced their first marriage at age 23. If the area beyond the Z score associated with age 23 is 0.24, what proportion of respondents experienced their first marriage before age 23?

Ans: 0.24

Learning Objective: 5-4: Transform a Z score into proportion (or percentage) and vice versa

Cognitive Domain: Comprehension

Answer Location: Finding the Area Above a Positive Z Score or Below a Negative Z Score

Difficulty Level: Medium

 

  1. The mean age at first marriage for respondents in a survey is 23.33, with a standard deviation of 6.13. Suppose that a person experienced their first marriage at age 23. If the area beyond the Z-score associated with age 23 is 0.24, what proportion of respondents experienced their first marriage after age 23?

Ans: 0.26 + 0.50 = 0.76

Learning Objective: 5-2: Describe the properties of the normal distribution

Cognitive Domain: Comprehension

Answer Location: The Standard Normal Table

Difficulty Level: Medium

 

  1. The mean age at first marriage for respondents in a survey is 23.33, with a standard deviation of 6.13. Suppose that the proportion of area between the mean and two Z scores of ±0.35 is 0.14. Calculate the raw scores associated with these two Z scores. What proportion of respondents were first married between these two ages?

Ans: .25.5; 0.14 + 0.14 = 0.28

Learning Objective: 5-2: Describe the properties of the normal distribution | 5-3: Transform a raw score into standard (Z) score and vice versa

Cognitive Domain: Comprehension

Answer Location: The Standard Normal Table; Transforming a Raw Score into a Z Score

Difficulty Level: Medium

 

  1. The mean age at first marriage for respondents in a survey is 23.33, with a standard deviation of 6.13. The Z score associated with the top 5% of the distribution is approximately 1.65. What is the observed age at first marriage associated with this Z score?

Ans: 33.44

Learning Objective: 5-4: Transform a Z score into proportion (or percentage) and vice versa

Cognitive Domain: Application

Answer Location: Transforming Proportions and Percentages into Z Scores

Difficulty Level: Medium

 

  1. The mean age at first marriage for respondents in a survey is 23.33, with a standard deviation of 6.13. For a first age at marriage of 33.44, the proportion of area beyond the Z score associated with this age is 0.05 . What is the percentile rank for this score?

Ans: 95th percentile

Learning Objective: 5-5: Calculate and interpret the percentile rank of a score

Cognitive Domain: Application

Answer Location: Working with Percentiles in a Normal Distribution

Difficulty Level: Medium

 

  1. The mean number of siblings for respondents in a survey is 3.76 with a standard deviation of 3.18. Calculate the Z score associated with three siblings.

Ans: –.24

Learning Objective: 5-3: Transform a raw score into standard (Z) score and vice versa

Cognitive Domain: Application

Answer Location: Transforming a Raw Score into a Z Score

Difficulty Level: Easy

 

  1. The mean number of siblings for respondents in a survey is 3.76 with a standard deviation of 3.18. Calculate the Z score associated with three siblings and provide a substantive interpretation of this quantity.

Ans: Three siblings is –.24 standard deviations below the mean number of siblings.

Learning Objective: 5-3: Transform a raw score into standard (Z) score and vice versa

Cognitive Domain: Comprehension

Answer Location: Transforming a Raw Score into a Z Score

Difficulty Level: Medium

 

  1. The mean number of siblings for respondents in a survey is 3.76 with a standard deviation of 3.18. Calculate the Z score associated with two siblings.

Ans: –.55

Learning Objective: 5-3: Transform a raw score into standard (Z) score and vice versa

Cognitive Domain: Application

Answer Location: Transforming a Raw Score into a Z Score

Difficulty Level: Easy

 

  1. The mean number of siblings for respondents in a survey is 3.76 with a standard deviation of 3.18. The standard normal table reports the following information in the table below. Calculate the proportion of respondents who had more than two siblings.
Number of Siblings Proportion of Area between Mean and Z Proportion of Area beyond Z
2 .21 .29
3 .09 .41

Ans: .50 + .21 = .71

Learning Objective: 5-2: Describe the properties of the normal distribution

Cognitive Domain: Application

Answer Location: Area Under the Normal Curve

Difficulty Level: Medium

 

  1. The mean number of siblings for respondents in a survey is 3.76 with a standard deviation of 3.18. The standard normal table reports the following information in the table below. Calculate the proportion of respondents who had between two and three siblings.
Number of Siblings Proportion of Area between Mean and Z Proportion of Area beyond Z
2 .21 .29
3 .09 .41

Ans: .21 – .09 = .12

Learning Objective: 5-2: Describe the properties of the normal distribution

Cognitive Domain: Application

Answer Location: Area Under the Normal Curve

Difficulty Level: Medium

 

  1. The mean number of siblings for respondents in a survey is 3.76 with a standard deviation of 3.18. The standard normal table reports the following information in the table below. Calculate the percentile rank for three siblings.
Number of Siblings Proportion of Area between Mean and Z Proportion of Area beyond Z
2 .21 .29
3 .09 .41

Ans: 41st percentile

Learning Objective: 5-5: Calculate and interpret the percentile rank of a score

Cognitive Domain: Application

Answer Location: Working with Percentiles in a Normal Distribution

Difficulty Level: Medium

 

  1. In a normal distribution with a mean of 3.76 and a standard deviation of 3.18, how many standard deviations from the mean is the 95th percentile?

Ans: 1.65

Learning Objective: 5-5: Calculate and interpret the percentile rank of a score

Cognitive Domain: Application

Answer Location: Working with Percentiles in a Normal Distribution

Difficulty Level: Medium

 

  1. Scores for an exam are normally distributed with a mean of 235 and a standard deviation of 52. How high must an individual score to be in the highest 10%?

Ans: 302 or higher

Learning Objective: 5-4: Transform a Z score into proportion (or percentage) and vice versa

Cognitive Domain: Application

Answer Location: Transforming Proportions and Percentages into Z Scores

Difficulty Level: Medium

 

  1. Scores for an exam are normally distributed with a mean of 235 and a standard deviation of 52. Identify the scores which correspond to the bottom 5%?

Ans: 142.2 or lower

Learning Objective: 5-4: Transform a Z score into proportion (or percentage) and vice versa

Cognitive Domain: Application

Answer Location: Transforming Proportions and Percentages into Z Scores

Difficulty Level: Medium

 

  1. Scores for an exam are normally distributed with a mean of 235 and a standard deviation of 52. What is the percentile rank of a raw score 287?

Ans: 84th percentile rank

Learning Objective: 5-5: Calculate and interpret the percentile rank of a score

Cognitive Domain: Application

Answer Location: Working with Percentiles in a Normal Distribution

Difficulty Level: Medium

 

  1. Scores for an exam are normally distributed with a mean of 235 and a standard deviation of 52. What is the percentile rank of a raw score 155?

Ans: 6th percentile rank

Learning Objective: 5-5: Calculate and interpret the percentile rank of a score

Cognitive Domain: Application

Answer Location: Working with Percentiles in a Normal Distribution

Difficulty Level: Medium

 

  1. The annual salaries of employees in a large company are normally distributed with a mean of $50,000 and a standard deviation of $20,000. What percent of people earn between $45,000 and $65,000?

Ans: 37.20%

Learning Objective: 5-4: Transform a Z score into proportion (or percentage) and vice versa

Cognitive Domain: Application

Answer Location: Transforming a Raw Score into a Z Score

Difficulty Level: Medium

 

 

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