Unit 6: The Normal Distribution - Practice Quiz

PSY115 — Statistical Methods For Psychological Research 60 Questions
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1 What is the general shape of a normal curve?

introduction to normal curve Easy
A. Bell-shaped
B. Flat-shaped
C. J-shaped
D. U-shaped

2 In a perfectly normal distribution, where is the highest point of the curve?

the nature of the normal curve Easy
A. At the maximum score
B. At the minimum score
C. At the far right tail
D. At the mean

3 What does NPC commonly stand for in statistics?

characteristics of NPC Easy
A. Negative Probability Coefficient
B. Normal Population Category
C. Normal Probability Curve
D. Numerical Percentage Calculation

4 Which statement describes the symmetry of a normal probability curve?

characteristics of NPC Easy
A. It is always higher on the right
B. It has no central point
C. It is always higher on the left
D. It is symmetric around the mean

5 In a normal distribution, the mean, median, and mode are:

characteristics of NPC Easy
A. Equal
B. All negative
C. Located at opposite ends
D. Always different

6 What happens to the normal curve as it extends farther from the mean?

the nature of the normal curve Easy
A. It changes into a rectangle
B. It becomes a straight line
C. It approaches the baseline
D. It rises to its peak

7 What is the total area under a normal probability curve?

characteristics of NPC Easy
A.
B.
C.
D.

8 A normal curve can be used as a model for which type of distribution?

the normal curve as a model for sampling distributions Easy
A. Sampling distributions
B. Only text responses
C. Only ranked categories
D. Only individual names

9 According to the Central Limit Theorem, the sampling distribution of a mean tends to become approximately normal when:

the normal curve as a model for sampling distributions Easy
A. Every score is identical
B. The sample size is sufficiently large
C. The population has no variation
D. The sample contains only one score

10 What does a sampling distribution describe?

the normal curve as a model for sampling distributions Easy
A. Names of people in one sample
B. Scores from one individual only
C. Values of a statistic from many samples
D. The questions used in a test

11 What does skewness describe?

skewness and types Easy
A. The width of a questionnaire
B. The total number of scores
C. The asymmetry of a distribution
D. The average measurement unit

12 A distribution with a longer tail toward higher scores is called:

skewness and types Easy
A. Bimodal
B. Perfectly uniform
C. Negatively skewed
D. Positively skewed

13 A distribution with a longer tail toward lower scores is called:

skewness and types Easy
A. Rectangular
B. Positively skewed
C. Perfectly normal
D. Negatively skewed

14 What is the skewness of a perfectly symmetric normal distribution?

skewness and types Easy
A.
B.
C.
D.

15 What does kurtosis describe?

kurtosis and types Easy
A. The peakedness of a distribution
B. The direction of a score scale
C. The number of variables studied
D. The sample's response rate

16 A distribution that is more peaked than the normal curve is called:

kurtosis and types Easy
A. Mesokurtic
B. Bivariate
C. Platykurtic
D. Leptokurtic

17 A distribution that is flatter than the normal curve is called:

kurtosis and types Easy
A. Leptokurtic
B. Unimodal
C. Platykurtic
D. Mesokurtic

18 A distribution with kurtosis similar to the normal curve is called:

kurtosis and types Easy
A. Leptokurtic
B. Asymmetrical
C. Mesokurtic
D. Platykurtic

19 Approximately what percentage of scores in a normal distribution lies within one standard deviation of the mean?

characteristics of NPC Easy
A. About 99.9%
B. About 68%
C. About 25%
D. About 50%

20 Which measure indicates how spread out scores are around the mean?

characteristics of NPC Easy
A. Mode
B. Skewness
C. Standard deviation
D. Median

21 A distribution has a mean of 50 and a standard deviation of 8. In a perfectly normal distribution, what is the relationship among the mean, median, and mode?

the nature of the normal curve Medium
A. The mode is greater than the mean
B. The mean is greater than the median
C. The mean, median, and mode are equal
D. The median is greater than the mode

22 In a normal distribution with and , which score is located one standard deviation above the mean?

the nature of the normal curve Medium
A.
B.
C.
D.

23 Why does the total area under a normal curve equal ?

the nature of the normal curve Medium
A. It represents the total probability of all possible scores
B. It represents the percentage of scores above the mean
C. It represents the number of standard deviations
D. It represents the difference between the mean and mode

24 A score of indicates that a score is:

introduction to normal curve Medium
A. 1.50 units below the mean
B. 1.50 standard deviations below the mean
C. 1.50 standard deviations above the mean
D. Equal to the sample mean

25 A test score of comes from a distribution with and . What is the score's -value?

introduction to normal curve Medium
A.
B.
C.
D.

26 Approximately what proportion of observations in a normal distribution lies between and ?

introduction to normal curve Medium
A. About
B. About
C. About
D. About

27 For a normal probability curve, what proportion of the area lies above the mean?

characteristics of NPC Medium
A.
B.
C.
D.

28 Which statement best describes the tails of a normal probability curve?

characteristics of NPC Medium
A. They are concentrated only around the mean
B. They contain exactly half of the total area
C. They stop sharply at one standard deviation
D. They approach the horizontal axis but never touch it

29 A normal distribution has and . Approximately what percentage of scores falls between and ?

characteristics of NPC Medium
A. About
B. About
C. About
D. About

30 According to the central limit theorem, the sampling distribution of the mean tends to become approximately normal when:

the normal curve as a model for sampling distributions Medium
A. The sample size becomes sufficiently large
B. The population contains only normally distributed scores
C. The population mean is exactly zero
D. Every sampled score equals the population mean

31 A population has . What is the standard error of the mean for samples of size ?

the normal curve as a model for sampling distributions Medium
A.
B.
C.
D.

32 If the sample size increases from to while population variability remains constant, what happens to the standard error of the mean?

the normal curve as a model for sampling distributions Medium
A. It becomes four times larger
B. It doubles
C. It remains unchanged
D. It is reduced by half

33 A population has mean and standard deviation . For samples of size , what is the mean and standard error of the sampling distribution of sample means?

the normal curve as a model for sampling distributions Medium
A. and
B. and
C. and
D. and

34 A sample mean has a -score of . What does this indicate about the sample mean?

the normal curve as a model for sampling distributions Medium
A. It is equal to two times the population standard deviation
B. It is two raw-score units below the population mean
C. It is two standard errors below the expected sample mean
D. It is two standard errors above the expected sample mean

35 A distribution has a long tail extending toward higher scores, while most scores cluster at the lower end. What type of skewness does it show?

skewness and types Medium
A. Bimodal skewness
B. Positive skewness
C. Zero skewness
D. Negative skewness

36 In a positively skewed distribution, which ordering is generally expected among the mean, median, and mode?

skewness and types Medium
A. Mode < median < mean
B. Mean < median < mode
C. Mean = median = mode
D. Median < mean < mode

37 A researcher finds that a few unusually low scores are pulling the distribution's mean below its median. Which type of skewness is most likely present?

skewness and types Medium
A. Symmetrical distribution
B. Positive skewness
C. Negative skewness
D. Uniform distribution

38 A distribution is more sharply peaked and has heavier tails than a normal distribution. How is it classified?

kurtosis and types Medium
A. Mesokurtic
B. Platykurtic
C. Leptokurtic
D. Negatively skewed

39 Which description best fits a platykurtic distribution?

kurtosis and types Medium
A. It is flatter with lighter tails than the normal curve
B. It has a longer tail only on the right side
C. It is sharper with heavier tails than the normal curve
D. It has equal frequencies for every possible score

40 A distribution has kurtosis similar to that of the normal distribution. Which label is appropriate?

kurtosis and types Medium
A. Bimodal
B. Mesokurtic
C. Leptokurtic
D. Platykurtic

41 A continuous distribution is perfectly symmetric about its mean, but its tails are substantially heavier than those of a normal distribution. Which conclusion is most defensible?

the nature of the normal curve Hard
A. It may be symmetric but leptokurtic
B. It cannot have a finite variance
C. It must be positively skewed
D. It must be platykurtic

42 For a truly normal variable , which transformation preserves normality while changing the mean and standard deviation?

the nature of the normal curve Hard
A.
B. , where
C.
D.

43 A normal distribution has mean and standard deviation . Which interval contains approximately the central of observations under the empirical rule?

the nature of the normal curve Hard
A.
B.
C.
D.

44 A population has mean and standard deviation . For samples of size , what is the approximate probability that the sample mean exceeds , assuming the normal model applies?

the normal curve as a model for sampling distributions Hard
A.
B.
C.
D.

45 Which statement best explains why the normal curve can model the sampling distribution of a mean even when the population itself is not normal?

the normal curve as a model for sampling distributions Hard
A. The sample standard deviation always equals the population standard deviation
B. The sample mean removes all population skewness
C. The central limit theorem supports approximate normality as sample size grows
D. Averaging makes every individual observation normally distributed

46 A heavily right-skewed population is sampled with . Which inference about the sampling distribution of is most appropriate?

the normal curve as a model for sampling distributions Hard
A. It is guaranteed to be right-skewed in exactly the population's shape
B. It is guaranteed to be normal
C. Normality may be a poor approximation unless additional conditions support it
D. Its mean is necessarily larger than the population mean

47 If sample size increases from to while population variability remains unchanged, how does the standard error of the mean change?

the normal curve as a model for sampling distributions Hard
A. It becomes four times larger
B. It remains unchanged
C. It doubles
D. It is halved

48 A score of comes from a distribution with mean and standard deviation . What is its standard score, and how should it be interpreted?

introduction to normal curve Hard
A. , eight units above the mean
B. , twelve standard deviations above the mean
C. , one point above the mean
D. , one and a half standard deviations above the mean

49 Two normal distributions have different means but identical standard deviations. For a fixed raw-score distance above each mean, which statement is correct?

introduction to normal curve Hard
A. The comparison is impossible without knowing the sample size
B. The score from the larger-mean distribution has the larger -score
C. The corresponding -scores are equal
D. The score from the smaller-mean distribution has the larger -score

50 For a standard normal variable , which expression is equivalent to ?

introduction to normal curve Hard
A.
B.
C.
D.

51 A distribution has mean , median , and mode . Which description is most consistent with these values?

skewness and types Hard
A. Negatively skewed
B. Approximately symmetric
C. Uniformly distributed
D. Positively skewed

52 A researcher log-transforms a strongly right-skewed reaction-time variable and obtains a distribution that is nearly symmetric. What has most likely occurred?

skewness and types Hard
A. The transformation changed a continuous variable into a categorical one
B. The transformation guaranteed a normal distribution
C. The transformation compressed the upper tail
D. The transformation increased positive skewness

53 Which pattern would most strongly suggest negative skewness in a psychological test-score distribution?

skewness and types Hard
A. Mean median mode
B. Mode median mean
C. Mean median mode
D. Equal frequencies across all score intervals

54 A distribution has skewness close to zero, but a histogram shows two equally sized peaks located symmetrically around the center. Which conclusion is best?

skewness and types Hard
A. It is necessarily positively skewed
B. It is necessarily normal
C. It must have zero kurtosis
D. It is symmetric but may be bimodal

55 Relative to a normal distribution, a leptokurtic distribution is generally characterized by which combination?

kurtosis and types Hard
A. A flatter center and lighter tails
B. A sharper center and heavier tails
C. Perfect symmetry with no extreme observations
D. Zero variance and a single observed value

56 A software package reports excess kurtosis of . What is the appropriate classification relative to the normal distribution?

kurtosis and types Hard
A. Mesokurtic
B. Platykurtic
C. Positively skewed
D. Leptokurtic

57 Which statement correctly distinguishes skewness from kurtosis?

kurtosis and types Hard
A. Skewness measures asymmetry; kurtosis describes tail weight and concentration
B. Skewness measures spread; kurtosis measures the arithmetic mean
C. Skewness applies only to normal curves; kurtosis applies only to samples
D. Skewness and kurtosis are two names for the same statistic

58 Which property of the normal probability curve explains why the probability of observing exactly one specified value is zero in the continuous model?

characteristics of NPC Hard
A. The mean and median are identical
B. A single point has zero width and therefore zero area
C. The curve has infinite tails
D. The total area is one

59 A normal curve is transformed from raw scores to -scores. Which feature changes under this transformation?

characteristics of NPC Hard
A. Its total area
B. Its symmetry
C. Its bell-shaped form
D. Its numerical center and scale

60 Why does the normal probability curve never actually touch the horizontal axis, even though its height becomes extremely small in the tails?

characteristics of NPC Hard
A. Its variance becomes negative in the tails
B. Its total area is greater than one
C. Its density approaches zero asymptotically
D. Its mean moves indefinitely toward both tails