CNSL 503 Module 4 Problem Set Actual Exam
2026/2027 | Complete Exam-Style Questions
with Detailed Rationales | Pass Guaranteed – A+
Graded
Section 1: Normal Distribution Properties
Q1: A normal distribution is defined by which two parameters?
A. Median and mode
B. Range and variance
C. Mean and standard deviation [CORRECT]
D. Frequency and probability
Correct Answer: C
Rationale: Correct because a normal distribution can be defined by two parameters: the mean
and the standard deviation. This matches CNSL 503 Module 4 content on normal distribution
properties.
Q2: What is the total area under the normal curve?
A. 0.50
B. 0.95
C. 1.00 [CORRECT]
D. 2.00
Correct Answer: C
Rationale: Correct because the total area under the curve is equal to 1.00, representing 100%
of the data in the distribution.
Q3: According to the 68-95-99.7 rule, approximately what percentage of values fall within 2
standard deviations of the mean?
A. 68%
B. 95% [CORRECT]
C. 99.7%
D. 100%
Correct Answer: B
Rationale: Correct because the 68-95-99.7 rule states that 95% of values fall within 2 standard
deviations of the mean, 68% within 1 standard deviation, and 99.7% within 3 standard
deviations.
Q4: Which of the following is NOT a characteristic of a normal distribution?
A. Bell-shaped curve
B. Symmetrical
C. Bimodal [CORRECT]
D. Unimodal
Correct Answer: C
Rationale: Correct because a normal distribution is unimodal, not bimodal. The normal curve is
symmetric and unimodal, with the mean, median, and mode all located at the center.
, Q5: In a normal distribution, where are the mean, median, and mode located?
A. At the right tail
B. At the left tail
C. At the center [CORRECT]
D. At two different points
Correct Answer: C
Rationale: Correct because in a normal distribution, the mean, median, and mode are all located
at the center of the distribution due to its symmetry.
Q6: Approximately what percentage of data falls within 1 standard deviation of the mean in a
normal distribution?
A. 50%
B. 68% [CORRECT]
C. 95%
D. 99.7%
Correct Answer: B
Rationale: Correct because the 68-95-99.7 rule states that 68% of values fall within 1 standard
deviation of the mean in a normal distribution.
Q7: What does the 99.7% value in the 68-95-99.7 rule represent?
A. The percentage within 1 standard deviation
B. The percentage within 2 standard deviations
C. The percentage within 3 standard deviations [CORRECT]
D. The percentage outside the distribution
Correct Answer: C
Rationale: Correct because the 68-95-99.7 rule states that 99.7% of values fall within 3 standard
deviations of the mean in a normal distribution.
Section 2: Z-Score Calculations
Q8: What is the primary purpose of calculating a z-score?
A. To calculate the mean of a distribution
B. To understand a score's relative standing and standardize scores from different data sets
[CORRECT]
C. To find the mode of a distribution
D. To determine the range of the data
Correct Answer: B
Rationale: Correct because the primary purpose of calculating z-scores is to understand a
score's relative standing within a distribution and to standardize scores from different data sets
with different means.
Q9: What is the formula for converting a raw score to a z-score?
A. z = (μ - X) / σ
B. z = X + μ / σ
C. z = (X - μ) / σ [CORRECT]
D. z = σ / (X - μ)
Correct Answer: C
Rationale: Correct because the formula for converting a raw score to a z-score is z = (X - μ) / σ,
where X is the raw score, μ is the mean, and σ is the standard deviation.
2026/2027 | Complete Exam-Style Questions
with Detailed Rationales | Pass Guaranteed – A+
Graded
Section 1: Normal Distribution Properties
Q1: A normal distribution is defined by which two parameters?
A. Median and mode
B. Range and variance
C. Mean and standard deviation [CORRECT]
D. Frequency and probability
Correct Answer: C
Rationale: Correct because a normal distribution can be defined by two parameters: the mean
and the standard deviation. This matches CNSL 503 Module 4 content on normal distribution
properties.
Q2: What is the total area under the normal curve?
A. 0.50
B. 0.95
C. 1.00 [CORRECT]
D. 2.00
Correct Answer: C
Rationale: Correct because the total area under the curve is equal to 1.00, representing 100%
of the data in the distribution.
Q3: According to the 68-95-99.7 rule, approximately what percentage of values fall within 2
standard deviations of the mean?
A. 68%
B. 95% [CORRECT]
C. 99.7%
D. 100%
Correct Answer: B
Rationale: Correct because the 68-95-99.7 rule states that 95% of values fall within 2 standard
deviations of the mean, 68% within 1 standard deviation, and 99.7% within 3 standard
deviations.
Q4: Which of the following is NOT a characteristic of a normal distribution?
A. Bell-shaped curve
B. Symmetrical
C. Bimodal [CORRECT]
D. Unimodal
Correct Answer: C
Rationale: Correct because a normal distribution is unimodal, not bimodal. The normal curve is
symmetric and unimodal, with the mean, median, and mode all located at the center.
, Q5: In a normal distribution, where are the mean, median, and mode located?
A. At the right tail
B. At the left tail
C. At the center [CORRECT]
D. At two different points
Correct Answer: C
Rationale: Correct because in a normal distribution, the mean, median, and mode are all located
at the center of the distribution due to its symmetry.
Q6: Approximately what percentage of data falls within 1 standard deviation of the mean in a
normal distribution?
A. 50%
B. 68% [CORRECT]
C. 95%
D. 99.7%
Correct Answer: B
Rationale: Correct because the 68-95-99.7 rule states that 68% of values fall within 1 standard
deviation of the mean in a normal distribution.
Q7: What does the 99.7% value in the 68-95-99.7 rule represent?
A. The percentage within 1 standard deviation
B. The percentage within 2 standard deviations
C. The percentage within 3 standard deviations [CORRECT]
D. The percentage outside the distribution
Correct Answer: C
Rationale: Correct because the 68-95-99.7 rule states that 99.7% of values fall within 3 standard
deviations of the mean in a normal distribution.
Section 2: Z-Score Calculations
Q8: What is the primary purpose of calculating a z-score?
A. To calculate the mean of a distribution
B. To understand a score's relative standing and standardize scores from different data sets
[CORRECT]
C. To find the mode of a distribution
D. To determine the range of the data
Correct Answer: B
Rationale: Correct because the primary purpose of calculating z-scores is to understand a
score's relative standing within a distribution and to standardize scores from different data sets
with different means.
Q9: What is the formula for converting a raw score to a z-score?
A. z = (μ - X) / σ
B. z = X + μ / σ
C. z = (X - μ) / σ [CORRECT]
D. z = σ / (X - μ)
Correct Answer: C
Rationale: Correct because the formula for converting a raw score to a z-score is z = (X - μ) / σ,
where X is the raw score, μ is the mean, and σ is the standard deviation.
