MATH 110 INTRODUCTION TO STATISTICS CUMULATIVE FINAL EXAM COMPLETE
PRACTICE TEST BANK QUESTIONS AND ANSWERS | VERIFIED SOLUTIONS |
UPDATED 2026/2027 STUDY GUIDE
Examiner/Administrator: Portage Learning
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
MATH 110 INTRODUCTION TO STATISTICS
CUMULATIVE FINAL EXAMINATION
2026/2027 EDITION
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
COMPLETE PRACTICE EXAM
30 MULTIPLE-CHOICE QUESTIONS
EXACT OFFICIAL COUNT: 30 QUESTIONS
PASSING SCORE: 70%
TESTING TIME: 120 MINUTES
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
PORTAGE LEARNING || ALIGNED WITH CURRENT INTRODUCTION TO STATISTICS
CURRICULUM BLUEPRINTS || COMPREHENSIVE FINAL EXAM REVIEW GUIDE ||
PROFESSIONAL PRACTICE QUESTIONS AND ANSWERS || 100% VERIFIED
EDUCATIONAL SOLUTIONS || UPDATED 2026/2027 ACADEMIC EDITION || PREPARED
FOR ONLINE COLLEGE-LEVEL STATISTICS ASSESSMENT || ADVANCED PROBLEM-
SOLVING APPLICATIONS || PROFESSIONAL EXAMINATION PREPARATION MATERIAL
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Descriptive Statistics, Data Interpretation, and Probability
Q1. A researcher records the weekly study hours of a random sample of college
students and finds the distribution is strongly right-skewed because a few students
study exceptionally long hours. Which measure of central tendency would best
represent the typical weekly study time?
A. Mean because it includes all values
B. Median because it is resistant to extreme values
,C. Range because it measures variability
D. Standard deviation because it measures spread
Correct Answer: 🔴 B. Median because it is resistant to extreme values
Explanation: 🔹 The median is the preferred measure of center for skewed distributions
because it is less affected by extreme observations or outliers. In this scenario, a few
students studying unusually long hours pull the mean upward, making it less
representative of the “typical” student. The range and standard deviation measure
variability rather than central tendency, so they are inappropriate choices for describing
the center of the data set.
Q2. A data set has a mean of 50 and a standard deviation of 5. Assuming an
approximately normal distribution, approximately what percentage of observations fall
between 45 and 55?
A. 34%
B. 68%
C. 95%
D. 99.7%
Correct Answer: 🔴 B. 68%
Explanation: 🔹 According to the Empirical Rule for normal distributions, approximately
68% of observations lie within one standard deviation of the mean. Since 45 and 55 are
one standard deviation below and above the mean of 50, about 68% of the data fall
within this interval. The 95% interval corresponds to two standard deviations, while
99.7% corresponds to three standard deviations.
Q3. A professor wants to compare exam scores from two different classes that used
different grading scales. Which statistical measure should be used to standardize the
scores?
A. Interquartile range
B. Variance
,C. z-score
D. Percentile rank
Correct Answer: 🔴 C. z-score
Explanation: 🔹 A z-score converts raw values into standardized units based on the mean
and standard deviation. This allows comparison across different scales or distributions.
The interquartile range and variance measure spread, while percentile rank indicates
relative standing but does not standardize data mathematically in the same way.
Q4. In a frequency distribution, the class width is determined by:
A. Subtracting the lowest class limit from the highest class limit of the same class
B. Dividing the mean by the standard deviation
C. Multiplying the number of classes by the range
D. Subtracting the median from the mode
Correct Answer: 🔴 A. Subtracting the lowest class limit from the highest class limit
of the same class
Explanation: 🔹 The class width measures the size of each interval in a grouped
frequency distribution. It is found by subtracting the lower class limit from the upper
class limit or by comparing consecutive lower class limits. The other options do not
describe the construction of class intervals in statistical tables.
Q5. Which probability value represents an impossible event?
A. 0
B. 0.25
C. 0.5
D. 1
Correct Answer: 🔴 A. 0
Explanation: 🔹 Probabilities range from 0 to 1 inclusive. A probability of 0 means the
event cannot occur, while a probability of 1 indicates certainty. Values such as 0.25 and
0.5 represent events with partial likelihoods.
, Q6. A box contains 5 red balls, 3 blue balls, and 2 green balls. What is the probability
of randomly selecting a blue ball?
A. 1/10
B. 2/5
C. 3/10
D. 1/2
Correct Answer: 🔴 C. 3/10
Explanation: 🔹 Probability is calculated as favorable outcomes divided by total
outcomes. There are 3 blue balls out of 10 total balls, so the probability is 3/10. The
other answer choices either miscount the number of favorable outcomes or incorrectly
compute the denominator.
Q7. Two events are independent if:
A. They cannot occur together
B. The occurrence of one event does not affect the probability of the other
C. They have equal probabilities
D. Their probabilities add to 1
Correct Answer: 🔴 B. The occurrence of one event does not affect the probability
of the other
Explanation: 🔹 Independent events occur without influencing one another.
Mathematically, independent events satisfy the relationship P(A and B) = P(A) × P(B).
Mutually exclusive events cannot occur simultaneously, which differs from independence.
Equal probabilities and probabilities summing to 1 are unrelated conditions.
Q8. Which graphical display is most appropriate for illustrating the distribution of
quantitative continuous data?
A. Pie chart
B. Histogram
PRACTICE TEST BANK QUESTIONS AND ANSWERS | VERIFIED SOLUTIONS |
UPDATED 2026/2027 STUDY GUIDE
Examiner/Administrator: Portage Learning
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
MATH 110 INTRODUCTION TO STATISTICS
CUMULATIVE FINAL EXAMINATION
2026/2027 EDITION
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
COMPLETE PRACTICE EXAM
30 MULTIPLE-CHOICE QUESTIONS
EXACT OFFICIAL COUNT: 30 QUESTIONS
PASSING SCORE: 70%
TESTING TIME: 120 MINUTES
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
PORTAGE LEARNING || ALIGNED WITH CURRENT INTRODUCTION TO STATISTICS
CURRICULUM BLUEPRINTS || COMPREHENSIVE FINAL EXAM REVIEW GUIDE ||
PROFESSIONAL PRACTICE QUESTIONS AND ANSWERS || 100% VERIFIED
EDUCATIONAL SOLUTIONS || UPDATED 2026/2027 ACADEMIC EDITION || PREPARED
FOR ONLINE COLLEGE-LEVEL STATISTICS ASSESSMENT || ADVANCED PROBLEM-
SOLVING APPLICATIONS || PROFESSIONAL EXAMINATION PREPARATION MATERIAL
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Descriptive Statistics, Data Interpretation, and Probability
Q1. A researcher records the weekly study hours of a random sample of college
students and finds the distribution is strongly right-skewed because a few students
study exceptionally long hours. Which measure of central tendency would best
represent the typical weekly study time?
A. Mean because it includes all values
B. Median because it is resistant to extreme values
,C. Range because it measures variability
D. Standard deviation because it measures spread
Correct Answer: 🔴 B. Median because it is resistant to extreme values
Explanation: 🔹 The median is the preferred measure of center for skewed distributions
because it is less affected by extreme observations or outliers. In this scenario, a few
students studying unusually long hours pull the mean upward, making it less
representative of the “typical” student. The range and standard deviation measure
variability rather than central tendency, so they are inappropriate choices for describing
the center of the data set.
Q2. A data set has a mean of 50 and a standard deviation of 5. Assuming an
approximately normal distribution, approximately what percentage of observations fall
between 45 and 55?
A. 34%
B. 68%
C. 95%
D. 99.7%
Correct Answer: 🔴 B. 68%
Explanation: 🔹 According to the Empirical Rule for normal distributions, approximately
68% of observations lie within one standard deviation of the mean. Since 45 and 55 are
one standard deviation below and above the mean of 50, about 68% of the data fall
within this interval. The 95% interval corresponds to two standard deviations, while
99.7% corresponds to three standard deviations.
Q3. A professor wants to compare exam scores from two different classes that used
different grading scales. Which statistical measure should be used to standardize the
scores?
A. Interquartile range
B. Variance
,C. z-score
D. Percentile rank
Correct Answer: 🔴 C. z-score
Explanation: 🔹 A z-score converts raw values into standardized units based on the mean
and standard deviation. This allows comparison across different scales or distributions.
The interquartile range and variance measure spread, while percentile rank indicates
relative standing but does not standardize data mathematically in the same way.
Q4. In a frequency distribution, the class width is determined by:
A. Subtracting the lowest class limit from the highest class limit of the same class
B. Dividing the mean by the standard deviation
C. Multiplying the number of classes by the range
D. Subtracting the median from the mode
Correct Answer: 🔴 A. Subtracting the lowest class limit from the highest class limit
of the same class
Explanation: 🔹 The class width measures the size of each interval in a grouped
frequency distribution. It is found by subtracting the lower class limit from the upper
class limit or by comparing consecutive lower class limits. The other options do not
describe the construction of class intervals in statistical tables.
Q5. Which probability value represents an impossible event?
A. 0
B. 0.25
C. 0.5
D. 1
Correct Answer: 🔴 A. 0
Explanation: 🔹 Probabilities range from 0 to 1 inclusive. A probability of 0 means the
event cannot occur, while a probability of 1 indicates certainty. Values such as 0.25 and
0.5 represent events with partial likelihoods.
, Q6. A box contains 5 red balls, 3 blue balls, and 2 green balls. What is the probability
of randomly selecting a blue ball?
A. 1/10
B. 2/5
C. 3/10
D. 1/2
Correct Answer: 🔴 C. 3/10
Explanation: 🔹 Probability is calculated as favorable outcomes divided by total
outcomes. There are 3 blue balls out of 10 total balls, so the probability is 3/10. The
other answer choices either miscount the number of favorable outcomes or incorrectly
compute the denominator.
Q7. Two events are independent if:
A. They cannot occur together
B. The occurrence of one event does not affect the probability of the other
C. They have equal probabilities
D. Their probabilities add to 1
Correct Answer: 🔴 B. The occurrence of one event does not affect the probability
of the other
Explanation: 🔹 Independent events occur without influencing one another.
Mathematically, independent events satisfy the relationship P(A and B) = P(A) × P(B).
Mutually exclusive events cannot occur simultaneously, which differs from independence.
Equal probabilities and probabilities summing to 1 are unrelated conditions.
Q8. Which graphical display is most appropriate for illustrating the distribution of
quantitative continuous data?
A. Pie chart
B. Histogram
