1. The normal probability curve is also known as the:
A. Bell curve
B. Skewed curve
C. Chi-square curve
D. U-shaped curve
Answer: A. Bell curve
Explanation: The normal probability curve is symmetric and bell-shaped. It is called a bell curve because of its characteristic shape—highest at the center and tapering on both ends.
2. The total area under the normal probability curve is:
A. 0.5
B. 1.0
C. 100
D. Depends on the mean
Answer: B. 1.0
Explanation: The area under the NPC represents the total probability and is equal to 1 (or 100%).
3. In a normal distribution, the mean, median, and mode:
A. Are all different
B. Are not defined
C. Are equal
D. Cannot be calculated
Answer: C. Are equal
Explanation: One key property of a normal distribution is that mean = median = mode, and all are located at the center of the curve.
4. Which of the following is not a property of the normal curve?
A. It is symmetrical
B. It is asymptotic to the X-axis
C. It is skewed to the right
D. Mean, median, and mode are identical
Answer: C. It is skewed to the right
Explanation: The NPC is not skewed; it is perfectly symmetrical about the mean. Skewed curves are not normal.
5. What percentage of data lies within ±1 standard deviation from the mean in a normal distribution?
A. 50%
B. 68.26%
C. 95.44%
D. 99.72%
Answer: B. 68.26%
Explanation: In a normal distribution, approximately 68.26% of the data fall within ±1 standard deviation of the mean.
6. The tails of the normal curve:
A. Never touch the X-axis
B. Touch the X-axis at ±1 SD
C. End at ±3 SD
D. Are unequal in length
Answer: A. Never touch the X-axis
Explanation: The tails of the NPC approach the X-axis asymptotically, meaning they get closer but never actually touch it.
7. What is the shape of the normal distribution curve?
A. Rectangular
B. Skewed
C. Bell-shaped
D. Linear
Answer: C. Bell-shaped
Explanation: The normal curve is symmetrical and bell-shaped, with most scores clustering around the mean.
8. In a normal distribution, approximately what percentage of cases lie within ±2 standard deviations?
A. 68%
B. 75%
C. 95%
D. 99%
Answer: C. 95%
Explanation: Approximately 95.44% of the values lie within ±2 standard deviations in a normal curve.
9. Which statistical method assumes that the data are normally distributed?
A. Chi-square test
B. T-test
C. Median test
D. Sign test
Answer: B. T-test
Explanation: The t-test assumes normality of the population from which samples are drawn, especially in small samples.
10. A flatter normal curve indicates:
A. Lower variability
B. Higher variability
C. Zero variability
D. Negative skewness
Answer: B. Higher variability
Explanation: A flatter curve results from a larger standard deviation, indicating higher spread in the data.
11. Which of the following is used to transform a normal distribution into a standard normal distribution?
A. Median
B. Variance
C. Z-score
D. Mode
Answer: C. Z-score
Explanation: A Z-score standardizes a score by subtracting the mean and dividing by the standard deviation, converting it into a standard normal distribution (mean = 0, SD = 1).
12. The normal probability curve is used in educational measurement to:
A. Interpret raw scores
B. Set classroom rules
C. Conduct interviews
D. Select teaching methods
Answer: A. Interpret raw scores
Explanation: The NPC helps in converting raw scores into percentile ranks, standard scores, and comparing student performance.
13. If a distribution has more values on the left of the mean, it is:
A. Positively skewed
B. Negatively skewed
C. Normal
D. Leptokurtic
Answer: A. Positively skewed
Explanation: A distribution with a longer right tail (more values on the left) is positively skewed—not normal.
14. The height of the NPC at the mean is:
A. Minimum
B. Maximum
C. Zero
D. Negative
Answer: B. Maximum
Explanation: The curve reaches its peak (maximum height) at the mean, where most data points cluster.
15. Which measure best represents central tendency in a normal curve?
A. Mode
B. Median
C. Mean
D. All of the above
Answer: D. All of the above
Explanation: In a normal distribution, the mean, median, and mode coincide and all represent the center.
16. What kind of test scores typically follow a normal distribution?
A. Essay scores
B. Aptitude test scores
C. Oral test scores
D. Interview scores
Answer: B. Aptitude test scores
Explanation: Standardized aptitude test scores are typically normally distributed due to large and representative sampling.
17. A perfectly normal distribution has skewness of:
A. 1
B. –1
C. 0
D. 3
Answer: C. 0
Explanation: A skewness of 0 indicates perfect symmetry, which is a property of the NPC.
18. Which of the following is not a use of the NPC in education?
A. Standardization of test scores
B. Selection and placement
C. Identifying learning disabilities
D. Conducting viva exams
Answer: D. Conducting viva exams
Explanation: NPC is used in quantitative analysis, not in oral exams like viva.
19. What does the area between ±3 standard deviations represent in NPC?
A. 99.99%
B. 100%
C. 99.72%
D. 90%
Answer: C. 99.72%
Explanation: About 99.72% of the data lies within ±3 standard deviations of the mean in a normal distribution.
20. The normal curve is important in educational research because it:
A. Helps reduce marks
B. Helps in qualitative analysis
C. Assists in score comparison and interpretation
D. Only applies to IQ tests
Answer: C. Assists in score comparison and interpretation
Explanation: The NPC enables objective comparison, standardization, and interpretation of educational test scores.
21. In a standard normal distribution, the mean is:
A. 1
B. 0
C. -1
D. Cannot be determined
Answer: B. 0
Explanation: A standard normal distribution is a special case of NPC where the mean is 0 and standard deviation is 1.
22. In a normal curve, which of the following values of kurtosis indicates a mesokurtic curve?
A. 0
B. 1
C. 2
D. 3
Answer: D. 3
Explanation: A mesokurtic distribution, which is the standard normal curve, has a kurtosis value of 3.
23. A negatively skewed distribution has:
A. A long tail to the right
B. A long tail to the left
C. Symmetry around the mean
D. No peak
Answer: B. A long tail to the left
Explanation: A negatively skewed distribution has its tail extending to the left, with most scores on the higher end.
24. Which of the following is not true about normal distribution?
A. It is symmetrical
B. It is unimodal
C. Mean is greater than the median
D. It is bell-shaped
Answer: C. Mean is greater than the median
Explanation: In a normal distribution, mean = median = mode. If mean > median, it indicates positive skewness.
25. Which part of the normal curve is used to determine standard scores like Z-scores?
A. Central tendency
B. Tails
C. Area under the curve
D. Height of the peak
Answer: C. Area under the curve
Explanation: Standard scores are derived from the area under the NPC, indicating probability of scores within a given range.
26. The standard deviation in a standard normal distribution is:
A. 0
B. 1
C. 100
D. Equal to mean
Answer: B. 1
Explanation: In a standard normal distribution, the standard deviation is always 1.
27. In NPC, the middle 50% of the data falls approximately between which standard deviation range?
A. ±0.67 SD
B. ±1 SD
C. ±1.5 SD
D. ±2 SD
Answer: A. ±0.67 SD
Explanation: The middle 50% of values lie between approximately –0.674 and +0.674 SD from the mean.
28. Which of the following best describes a leptokurtic distribution compared to a normal distribution?
A. Flatter and wider
B. Higher peak and narrower tails
C. Perfectly bell-shaped
D. Skewed to the right
Answer: B. Higher peak and narrower tails
Explanation: Leptokurtic distributions have a sharp peak and thinner tails than the normal curve.
29. Which of the following percentile ranks corresponds to a Z-score of 0 in a normal distribution?
A. 25th percentile
B. 50th percentile
C. 75th percentile
D. 100th percentile
Answer: B. 50th percentile
Explanation: A Z-score of 0 represents the mean, and hence the 50th percentile in a normal distribution.
30. The normal curve helps teachers in:
A. Judging students’ handwriting
B. Comparing students’ performance
C. Conducting interviews
D. Planning field trips
Answer: B. Comparing students’ performance
Explanation: NPC allows conversion of raw scores to standardized scores, making student comparison objective and meaningful.
31. The most common application of normal distribution in psychological testing is:
A. Selecting research tools
B. Norm-referenced interpretation
C. Conducting experiments
D. Developing teaching methods
Answer: B. Norm-referenced interpretation
Explanation: Psychological and educational assessments often use NPC to compare individual scores to the norm group.
32. If a test score is 1.5 SD above the mean, the Z-score is:
A. –1.5
B. 1.5
C. 0.5
D. 2.5
Answer: B. 1.5
Explanation: Z-score is calculated as (X – Mean)/SD. A score 1.5 SD above the mean has a Z-score of +1.5.
33. If the NPC is skewed, which statistical methods may be inappropriate without transformation?
A. Correlation
B. T-tests and ANOVA
C. Frequency analysis
D. Data tabulation
Answer: B. T-tests and ANOVA
Explanation: These parametric tests assume normality. If data is skewed, results may be invalid unless data is transformed.
34. What is the shape of a platykurtic distribution?
A. Tall and sharp
B. Normal
C. Flat and wide
D. U-shaped
Answer: C. Flat and wide
Explanation: Platykurtic distributions are flatter and wider with less peakedness compared to a normal curve.
35. The normal curve is most useful in which type of evaluation?
A. Formative
B. Diagnostic
C. Summative
D. Norm-referenced
Answer: D. Norm-referenced
Explanation: Norm-referenced testing uses NPC to rank and compare student performance relative to others.
36. In NPC, if 5% of scores lie beyond +2 SD, the scores are considered:
A. Average
B. Below average
C. Exceptional or gifted
D. Skewed
Answer: C. Exceptional or gifted
Explanation: Scores beyond +2 SD are in the top 2.5% and often considered exceptional in education and psychology.
37. What is the utility of the normal curve in constructing educational tests?
A. It ensures equal difficulty
B. It helps to measure attitude
C. It guides in norming and interpreting scores
D. It replaces rubrics
Answer: C. It guides in norming and interpreting scores
Explanation: NPC is used in standardization of scores, setting cut-off points, and interpreting test results.
38. Z-scores are used in normal distribution to:
A. Convert scores into percentages
B. Rank scores based on skewness
C. Determine relative position of scores
D. Transform data into raw scores
Answer: C. Determine relative position of scores
Explanation: Z-scores show how far a score is from the mean in terms of standard deviations, identifying its relative position.
39. Which of the following tests is least affected by departure from normality?
A. T-test
B. ANOVA
C. Pearson correlation
D. Spearman rank correlation
Answer: D. Spearman rank correlation
Explanation: Spearman’s rho is a non-parametric test and doesn’t assume normal distribution, making it robust to skewed data.
40. Which term describes the “tail behavior” or extremity of values in a normal distribution?
A. Skewness
B. Peakness
C. Kurtosis
D. Symmetry
Answer: C. Kurtosis
Explanation: Kurtosis refers to the heaviness of the tails and the peakedness of a distribution.
41. A student scores at the 84th percentile in a normally distributed test. What is their approximate Z-score?
A. 0.5
B. 1.0
C. 1.5
D. 2.0
Answer: B. 1.0
Explanation: In a normal distribution, a Z-score of +1 corresponds approximately to the 84th percentile.
42. What is the percentile rank of a score that lies exactly at the mean of a normal distribution?
A. 0th percentile
B. 25th percentile
C. 50th percentile
D. 100th percentile
Answer: C. 50th percentile
Explanation: The mean divides the normal curve into two equal halves. A score at the mean lies at the 50th percentile.
43. In a normal curve, a Z-score of –2.0 indicates the score is:
A. 2 points below the mean
B. 2 standard deviations below the mean
C. Equal to the mean
D. 2 percentile points below the mean
Answer: B. 2 standard deviations below the mean
Explanation: A Z-score of –2.0 means the score is 2 SDs below the mean.
44. Which of the following is an advantage of using NPC in educational testing?
A. Allows random grading
B. Compares scores on different tests
C. Avoids the use of standard deviation
D. Makes qualitative evaluation easy
Answer: B. Compares scores on different tests
Explanation: By standardizing scores (using Z-scores), NPC allows meaningful comparison across tests with different scales.
45. If a test has a normal distribution, what proportion of students score above the mean?
A. 25%
B. 50%
C. 68%
D. 95%
Answer: B. 50%
Explanation: In a symmetrical NPC, the area under the curve is equally divided on both sides of the mean—50% above and 50% below.
46. Which type of score is most directly derived from the normal curve?
A. Grade point average
B. Raw score
C. Percentile score
D. Z-score
Answer: D. Z-score
Explanation: Z-scores are calculated using the properties of the normal curve (mean and standard deviation).
47. In classroom evaluation, the normal curve is useful for:
A. Essay scoring
B. Evaluating teacher behavior
C. Diagnosing student strengths and weaknesses
D. Setting cut-off marks for merit-based selection
Answer: D. Setting cut-off marks for merit-based selection
Explanation: NPC helps determine performance thresholds such as top 10%, bottom 10%, etc., for competitive purposes.
48. A student has a Z-score of +2. What can we infer about their performance?
A. Below average
B. Average
C. Moderately above average
D. Significantly above average
Answer: D. Significantly above average
Explanation: A Z-score of +2 places the student in the top 2.5% of the distribution, indicating exceptional performance.
49. If test scores are positively skewed, most students have:
A. High scores
B. Low scores
C. Equal scores
D. No scores
Answer: B. Low scores
Explanation: Positive skew means the tail extends to the right, indicating most scores are concentrated on the lower side.
50. A distribution that is not normally distributed is called:
A. Abnormal
B. Standard
C. Non-parametric
D. Parametric
Answer: C. Non-parametric
Explanation: Distributions that do not follow the normal curve are considered non-parametric and require non-parametric tests.
51. Which of the following measures is least influenced by skewness in data?
A. Mean
B. Median
C. Mode
D. Standard deviation
Answer: B. Median
Explanation: The median is a positional measure and is less affected by extreme scores or skewness compared to the mean.
52. When using the normal curve for educational guidance, counselors can:
A. Assign grades randomly
B. Identify student aptitudes
C. Change students’ scores
D. Ignore variability
Answer: B. Identify student aptitudes
Explanation: Standardized scores based on NPC help counselors in identifying student strengths and recommending career paths.
53. Which transformation makes a non-normal distribution more normal?
A. Addition
B. Subtraction
C. Logarithmic transformation
D. Multiplication
Answer: C. Logarithmic transformation
Explanation: Logarithmic (or square root) transformations are commonly used to reduce skewness and normalize data.
54. A distribution with a Z-score of –3 is considered:
A. Typical
B. Within average range
C. Extremely low performance
D. Not interpretable
Answer: C. Extremely low performance
Explanation: A Z-score of –3 places the score in the bottom 0.13% of the distribution—far below the mean.
55. In educational measurement, using normal distribution helps reduce:
A. Bias in test administration
B. Impact of qualitative traits
C. Subjectivity in interpretation
D. Cost of conducting exams
Answer: C. Subjectivity in interpretation
Explanation: NPC-based standard scores provide objective criteria to interpret and compare student performance.
56. Which of the following is not a limitation of the NPC in education?
A. Assumes perfect symmetry
B. Not suitable for all types of data
C. Assumes homogeneity
D. Encourages bias in scoring
Answer: D. Encourages bias in scoring
Explanation: NPC actually helps in reducing scoring bias by providing objective, standardized frameworks.
57. The term “asymptotic” in relation to the NPC means:
A. The curve touches the X-axis
B. The curve intersects the mean
C. The curve never touches the X-axis
D. The curve is flat
Answer: C. The curve never touches the X-axis
Explanation: The NPC approaches but never touches the X-axis, extending infinitely in both directions.
58. In the NPC, the highest frequency of scores is found at:
A. The mode
B. The mean
C. The median
D. All of the above
Answer: D. All of the above
Explanation: In a normal curve, mean = median = mode; hence, the highest frequency is at this central point.
59. Which term best describes the overall usefulness of NPC in education?
A. Diagnostic
B. Descriptive
C. Inferential
D. Normative
Answer: D. Normative
Explanation: NPC is foundational in norm-referenced testing, helping educators set benchmarks and interpret scores.
60. If a student’s Z-score is 0.00, then their raw score is:
A. Below average
B. Equal to the mean
C. Above average
D. Undefined
Answer: B. Equal to the mean
Explanation: A Z-score of 0 indicates the raw score is exactly at the mean of the distribution.