PORTAGE LEARNING STATISTICS MODULE 4 THE Z-TEST QUESTIONS AND ANSWERS
WITH COMPLETE SOLUTIONS | NEW UPDATE 2026!!!
Question 1
A frequency distribution that follows a bell-shaped, symmetrical, and unimodal curve is
officially known as a:
A) Bi-modal distribution
B) Skewed distribution
C) Normal curve
D) Chi-square distribution
E) Poisson distribution
Correct Answer: C) normal curve
Rationale: A normal curve is defined by its characteristic bell shape, where the data is
symmetrical around the center and contains only one peak (unimodal).
Question 2
In a perfectly normal distribution, where is the mean located on the curve?
A) At the far right tail
B) At the far left tail
C) In the middle of the curve
D) At the first standard deviation
E) It varies depending on the sample size
Correct Answer: C) middle of the curve
Rationale: Because the normal distribution is symmetrical, the arithmetic average (mean)
always falls exactly in the center, bisecting the curve into two equal halves.
Question 3
What is the mathematical relationship between the mean, median, and mode in a normal
distribution?
A) Mean > Median > Mode
B) Mode > Median > Mean
C) Mean = Median = Mode
D) The mean is twice the mode
E) There is no consistent relationship
Correct Answer: C) Mean = Median = Mode
Rationale: In a perfectly symmetrical, unimodal distribution, the point of highest frequency
(mode), the middle value (median), and the average (mean) all coincide at the same central
point.
Question 4
In a normal distribution, what happens to the frequency of scores as they move further away
from the mean?
A) The frequency increases
B) The frequency remains constant
, 2
C) The frequency decreases
D) The frequency becomes unpredictable
E) The frequency doubles for every standard deviation
Correct Answer: C) the lower the frequency
Rationale: The "tails" of a normal curve represent extreme values. As values deviate from
the mean, they become rarer, resulting in a lower frequency of occurrence.
Question 5
Scores that fall beyond two standard deviations from the mean in a normal distribution are
considered:
A) Highly common
B) To occur 50% of the time
C) To occur rarely
D) Impossible
E) The majority of the dataset
Correct Answer: C) scores beyond 2 standard deviations from the mean rarely occur
Rationale: According to the empirical rule, approximately 95% of data falls within 2
standard deviations; therefore, only 5% of scores fall beyond this point, making them rare.
Question 6
Where is the greatest frequency of data points clustered in a normal distribution?
A) At the extreme ends of the tails
B) Between 2 and 3 standard deviations
C) Around the mean
D) At the z-score of +3.0
E) Evenly across the entire x-axis
Correct Answer: C) clustered around the mean
Rationale: The "hump" of the bell curve is highest at the center, indicating that values near
the mean have the highest probability/frequency of occurring.
Question 7
How does a smaller standard deviation affect the shape of the normal distribution curve?
A) It makes the curve flatter
B) It creates a higher arc (taller/narrower)
C) It makes the curve asymmetrical
D) It creates a lower arc (shorter/wider)
E) It shifts the mean to the right
Correct Answer: B) higher arc
Rationale: A small standard deviation indicates that data points are close to the mean. This
results in a narrower, taller curve with a higher peak.
, 3
Question 8
A distribution with a larger standard deviation will result in a curve with a:
A) Higher arc
B) Skewed tail
C) Lower arc
D) Bi-modal peak
E) Vertical line
Correct Answer: C) lower arc
Rationale: A larger standard deviation means the data is more spread out from the mean,
causing the bell shape to stretch horizontally and flatten vertically (a lower arc).
Question 9
Which two parameters are required to fully define a specific normal distribution?
A) Range and Mode
B) Median and Variance
C) Mean and Standard Deviation
D) Sample size and Alpha level
E) Z-score and P-value
Correct Answer: C) mean and standard deviation
Rationale: The mean determines the location of the center of the curve, while the standard
deviation determines the spread or width of the curve.
Question 10
The total area under the normal curve represents the total relative frequency of a distribution and
is equal to:
A) 0.50 or 50%
B) 0.95 or 95%
C) 1.00 or 100%
D) 0.68 or 68%
E) 1.96
Correct Answer: C) 1.00 or 100%
Rationale: The area under the curve encompasses every possible outcome in the
distribution, representing the entire population (100%).
Question 11
Because the normal curve is symmetrical, what can be said about the distribution of scores
relative to the mean?
A) 100% of scores fall above the mean
B) More scores fall below the mean than above
C) An equal number of distributions fall above and below the mean
D) Scores only fall within 1 standard deviation
WITH COMPLETE SOLUTIONS | NEW UPDATE 2026!!!
Question 1
A frequency distribution that follows a bell-shaped, symmetrical, and unimodal curve is
officially known as a:
A) Bi-modal distribution
B) Skewed distribution
C) Normal curve
D) Chi-square distribution
E) Poisson distribution
Correct Answer: C) normal curve
Rationale: A normal curve is defined by its characteristic bell shape, where the data is
symmetrical around the center and contains only one peak (unimodal).
Question 2
In a perfectly normal distribution, where is the mean located on the curve?
A) At the far right tail
B) At the far left tail
C) In the middle of the curve
D) At the first standard deviation
E) It varies depending on the sample size
Correct Answer: C) middle of the curve
Rationale: Because the normal distribution is symmetrical, the arithmetic average (mean)
always falls exactly in the center, bisecting the curve into two equal halves.
Question 3
What is the mathematical relationship between the mean, median, and mode in a normal
distribution?
A) Mean > Median > Mode
B) Mode > Median > Mean
C) Mean = Median = Mode
D) The mean is twice the mode
E) There is no consistent relationship
Correct Answer: C) Mean = Median = Mode
Rationale: In a perfectly symmetrical, unimodal distribution, the point of highest frequency
(mode), the middle value (median), and the average (mean) all coincide at the same central
point.
Question 4
In a normal distribution, what happens to the frequency of scores as they move further away
from the mean?
A) The frequency increases
B) The frequency remains constant
, 2
C) The frequency decreases
D) The frequency becomes unpredictable
E) The frequency doubles for every standard deviation
Correct Answer: C) the lower the frequency
Rationale: The "tails" of a normal curve represent extreme values. As values deviate from
the mean, they become rarer, resulting in a lower frequency of occurrence.
Question 5
Scores that fall beyond two standard deviations from the mean in a normal distribution are
considered:
A) Highly common
B) To occur 50% of the time
C) To occur rarely
D) Impossible
E) The majority of the dataset
Correct Answer: C) scores beyond 2 standard deviations from the mean rarely occur
Rationale: According to the empirical rule, approximately 95% of data falls within 2
standard deviations; therefore, only 5% of scores fall beyond this point, making them rare.
Question 6
Where is the greatest frequency of data points clustered in a normal distribution?
A) At the extreme ends of the tails
B) Between 2 and 3 standard deviations
C) Around the mean
D) At the z-score of +3.0
E) Evenly across the entire x-axis
Correct Answer: C) clustered around the mean
Rationale: The "hump" of the bell curve is highest at the center, indicating that values near
the mean have the highest probability/frequency of occurring.
Question 7
How does a smaller standard deviation affect the shape of the normal distribution curve?
A) It makes the curve flatter
B) It creates a higher arc (taller/narrower)
C) It makes the curve asymmetrical
D) It creates a lower arc (shorter/wider)
E) It shifts the mean to the right
Correct Answer: B) higher arc
Rationale: A small standard deviation indicates that data points are close to the mean. This
results in a narrower, taller curve with a higher peak.
, 3
Question 8
A distribution with a larger standard deviation will result in a curve with a:
A) Higher arc
B) Skewed tail
C) Lower arc
D) Bi-modal peak
E) Vertical line
Correct Answer: C) lower arc
Rationale: A larger standard deviation means the data is more spread out from the mean,
causing the bell shape to stretch horizontally and flatten vertically (a lower arc).
Question 9
Which two parameters are required to fully define a specific normal distribution?
A) Range and Mode
B) Median and Variance
C) Mean and Standard Deviation
D) Sample size and Alpha level
E) Z-score and P-value
Correct Answer: C) mean and standard deviation
Rationale: The mean determines the location of the center of the curve, while the standard
deviation determines the spread or width of the curve.
Question 10
The total area under the normal curve represents the total relative frequency of a distribution and
is equal to:
A) 0.50 or 50%
B) 0.95 or 95%
C) 1.00 or 100%
D) 0.68 or 68%
E) 1.96
Correct Answer: C) 1.00 or 100%
Rationale: The area under the curve encompasses every possible outcome in the
distribution, representing the entire population (100%).
Question 11
Because the normal curve is symmetrical, what can be said about the distribution of scores
relative to the mean?
A) 100% of scores fall above the mean
B) More scores fall below the mean than above
C) An equal number of distributions fall above and below the mean
D) Scores only fall within 1 standard deviation
