MATH 110 MODULE 7: NORMAL
DISTRIBUTION AND SAMPLING
DISTRIBUTIONS 2026/2027 UPDATE.
JUST RELEASED
1. Which of the following is NOT a property of a normal distribution?
A. The distribution is symmetric about its mean.
B. The distribution is defined by the range and the interquartile range.
C. The mean, median, and mode are all equal.
D. The total area under the curve is exactly 1.
Answer: B
Conceptual Explanation: A normal distribution is defined by its mean and standard
deviation, not its range or interquartile range.
2. In a standard normal distribution, what percentage of data falls within two standard
deviations of the mean?
A. Approximately 68%
B. Approximately 99.7%
C. Approximately 95%
D. Exactly 50%
,Answer: C
Conceptual Explanation: According to the Empirical Rule, approximately 95% of the
observations in a normal distribution fall within two standard deviations of the mean.
3. Given a normal distribution with a mean of 50 and a standard deviation of 10, what is the
Z-score for an X value of 35?
A. 2.0
B. 1.5
C. -1.0
D. -1.5
Answer: D
Conceptual Explanation: The Z-score formula is (X - mu) / sigma. Here, (35 - 50) / 10 = -
= -1.5.
4. What is the area under the standard normal curve to the left of Z = 0?
A. 0.0
B. 0.5
C. 1.0
D. -0.5
Answer: B
, Conceptual Explanation: Since the normal distribution is symmetric about the mean
(Z=0), exactly 50% of the area lies to the left of the mean.
5. If a distribution of sample means is created from a population with a mean of 100 and a
standard deviation of 20 using a sample size of n=25, what is the standard error of the mean?
A. 20
B. 4
C. 0.8
D. 5
Answer: B
Conceptual Explanation: The standard error of the mean is sigma / sqrt(n). Here, 20 /
sqrt(25) = = 4.
6. The Central Limit Theorem states that as the sample size increases, the sampling
distribution of the sample mean approaches:
A. A uniform distribution
B. The distribution of the population
C. A binomial distribution
D. A normal distribution
Answer: D
DISTRIBUTION AND SAMPLING
DISTRIBUTIONS 2026/2027 UPDATE.
JUST RELEASED
1. Which of the following is NOT a property of a normal distribution?
A. The distribution is symmetric about its mean.
B. The distribution is defined by the range and the interquartile range.
C. The mean, median, and mode are all equal.
D. The total area under the curve is exactly 1.
Answer: B
Conceptual Explanation: A normal distribution is defined by its mean and standard
deviation, not its range or interquartile range.
2. In a standard normal distribution, what percentage of data falls within two standard
deviations of the mean?
A. Approximately 68%
B. Approximately 99.7%
C. Approximately 95%
D. Exactly 50%
,Answer: C
Conceptual Explanation: According to the Empirical Rule, approximately 95% of the
observations in a normal distribution fall within two standard deviations of the mean.
3. Given a normal distribution with a mean of 50 and a standard deviation of 10, what is the
Z-score for an X value of 35?
A. 2.0
B. 1.5
C. -1.0
D. -1.5
Answer: D
Conceptual Explanation: The Z-score formula is (X - mu) / sigma. Here, (35 - 50) / 10 = -
= -1.5.
4. What is the area under the standard normal curve to the left of Z = 0?
A. 0.0
B. 0.5
C. 1.0
D. -0.5
Answer: B
, Conceptual Explanation: Since the normal distribution is symmetric about the mean
(Z=0), exactly 50% of the area lies to the left of the mean.
5. If a distribution of sample means is created from a population with a mean of 100 and a
standard deviation of 20 using a sample size of n=25, what is the standard error of the mean?
A. 20
B. 4
C. 0.8
D. 5
Answer: B
Conceptual Explanation: The standard error of the mean is sigma / sqrt(n). Here, 20 /
sqrt(25) = = 4.
6. The Central Limit Theorem states that as the sample size increases, the sampling
distribution of the sample mean approaches:
A. A uniform distribution
B. The distribution of the population
C. A binomial distribution
D. A normal distribution
Answer: D
