,MATH 110 Module 5 Exam - Introduction to
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1. Which of the following correctly describes the shape of a normal distribution?
A) It is skewed to the right
B) It is skewed to the left
C) It is perfectly symmetric and bell-shaped
D) It is uniform
Correct Answer: C) It is perfectly symmetric and bell-shaped
Rationale: The normal distribution is defined by its symmetric, bell-shaped curve, with the mean,
median, and mode all equal and located at the center. Skewed distributions have a longer tail on one
side, while a uniform distribution has a constant height.
2. The total area under the curve of any normal distribution is equal to:
A) 0.5
B) 1.0
C) 3.1416
D) 100
Correct Answer: B) 1.0
Rationale: The total area under any probability density function, including the normal curve, equals 1,
representing the total probability of all possible outcomes. 0.5 would be half the area, π is unrelated,
and 100 is a percentage misinterpretation.
3. The standard normal distribution has a mean of ____ and a standard deviation of ____.
A) 0, 1
,B) 1, 0
C) 0, 0
D) 1, 1
Correct Answer: A) 0, 1
Rationale: By definition, the standard normal distribution has a mean of 0 and a standard deviation of
1. This standardization allows for comparison across different normal distributions.
4. A z-score represents:
A) The probability of a value occurring
B) The number of standard deviations a value is from the mean
C) The percentage of data below a value
D) The raw score in a dataset
Correct Answer: B) The number of standard deviations a value is from the mean
Rationale: The z-score is calculated as (x - μ)/σ, indicating how many standard deviations a data point
is from the mean. Probability and percentage require additional calculations, and the raw score is the
original value.
5. A data value has a z-score of -2.0. This means the value is:
A) 2 standard deviations above the mean
B) 2 standard deviations below the mean
C) 2 times the mean
D) 2% below the mean
Correct Answer: B) 2 standard deviations below the mean
, Rationale: A negative z-score indicates the value is below the mean, and the magnitude shows the
number of standard deviations. A positive z-score would indicate above the mean.
6. What is the z-score for a raw score of 85 from a population with a mean of 70 and a standard
deviation of 10?
A) -1.5
B) 0.5
C) 1.5
D) 8.5
Correct Answer: C) 1.5
Rationale: z = (x - μ) / σ = (85 - 70) / 10 = = 1.5. Option A is for x=55, B is for x=75, and D is the
raw score divided by 10 incorrectly.
7. The 68-95-99.7 rule applies to which distribution?
A) Any distribution
B) Binomial distribution
C) Normal distribution
D) Uniform distribution
Correct Answer: C) Normal distribution
Rationale: The empirical rule (68-95-99.7) specifically applies to normal distributions, stating that
approximately 68%, 95%, and 99.7% of data fall within 1, 2, and 3 standard deviations of the mean,
respectively.
8. According to the empirical rule, approximately what percentage of data falls within ±2 standard
deviations of the mean in a normal distribution?
A) 68%
B) 75%
Statistics Portage Learning - Latest (26/27)
(PDF)
1. Which of the following correctly describes the shape of a normal distribution?
A) It is skewed to the right
B) It is skewed to the left
C) It is perfectly symmetric and bell-shaped
D) It is uniform
Correct Answer: C) It is perfectly symmetric and bell-shaped
Rationale: The normal distribution is defined by its symmetric, bell-shaped curve, with the mean,
median, and mode all equal and located at the center. Skewed distributions have a longer tail on one
side, while a uniform distribution has a constant height.
2. The total area under the curve of any normal distribution is equal to:
A) 0.5
B) 1.0
C) 3.1416
D) 100
Correct Answer: B) 1.0
Rationale: The total area under any probability density function, including the normal curve, equals 1,
representing the total probability of all possible outcomes. 0.5 would be half the area, π is unrelated,
and 100 is a percentage misinterpretation.
3. The standard normal distribution has a mean of ____ and a standard deviation of ____.
A) 0, 1
,B) 1, 0
C) 0, 0
D) 1, 1
Correct Answer: A) 0, 1
Rationale: By definition, the standard normal distribution has a mean of 0 and a standard deviation of
1. This standardization allows for comparison across different normal distributions.
4. A z-score represents:
A) The probability of a value occurring
B) The number of standard deviations a value is from the mean
C) The percentage of data below a value
D) The raw score in a dataset
Correct Answer: B) The number of standard deviations a value is from the mean
Rationale: The z-score is calculated as (x - μ)/σ, indicating how many standard deviations a data point
is from the mean. Probability and percentage require additional calculations, and the raw score is the
original value.
5. A data value has a z-score of -2.0. This means the value is:
A) 2 standard deviations above the mean
B) 2 standard deviations below the mean
C) 2 times the mean
D) 2% below the mean
Correct Answer: B) 2 standard deviations below the mean
, Rationale: A negative z-score indicates the value is below the mean, and the magnitude shows the
number of standard deviations. A positive z-score would indicate above the mean.
6. What is the z-score for a raw score of 85 from a population with a mean of 70 and a standard
deviation of 10?
A) -1.5
B) 0.5
C) 1.5
D) 8.5
Correct Answer: C) 1.5
Rationale: z = (x - μ) / σ = (85 - 70) / 10 = = 1.5. Option A is for x=55, B is for x=75, and D is the
raw score divided by 10 incorrectly.
7. The 68-95-99.7 rule applies to which distribution?
A) Any distribution
B) Binomial distribution
C) Normal distribution
D) Uniform distribution
Correct Answer: C) Normal distribution
Rationale: The empirical rule (68-95-99.7) specifically applies to normal distributions, stating that
approximately 68%, 95%, and 99.7% of data fall within 1, 2, and 3 standard deviations of the mean,
respectively.
8. According to the empirical rule, approximately what percentage of data falls within ±2 standard
deviations of the mean in a normal distribution?
A) 68%
B) 75%
