MATH 1280 FINAL EXAM ACTUAL EXAM 2025 ALL
QUESTIONS AND CORRECT ANSWERS (PROFESSOR
VERIFIED) | LATEST EDITION | REAL EXAM
Introductory Statistics | Key Domains: Data Collection & Sampling, Descriptive Statistics,
Probability, Random Variables & Distributions, Sampling Distributions, Estimation, Hypothesis
Testing, Correlation & Regression, and Statistical Software Applications | Expert-Aligned Structure |
Exam-Ready Format
Introduction
This structured Math 1280 (Introductory Statistics) Final Exam for 2025 provides a comprehensive
set of high-quality exam-style questions with correct answers and rationales. It emphasizes core
statistical concepts, calculation methods, data interpretation, and proper application of statistical
tests critical for academic and practical success.
Answer Format
All correct answers must appear in bold and cyan blue, accompanied by concise rationales
explaining statistical reasoning, formula application, and why alternative options are
mathematically or conceptually incorrect.
1. A researcher wants to estimate the average height of students at a university. She selects 50
students from a list using a random number generator. This is an example of:
A. Convenience sampling
B. Stratified sampling
C. Simple random sampling
D. Cluster sampling
,Rationale: Simple random sampling involves selecting individuals entirely at random from the
population, where each member has an equal chance of being chosen. Using a random number
generator on a complete list satisfies this condition. Convenience sampling uses readily available
subjects, while stratified and cluster sampling involve dividing the population first.
2. The median of the data set {3, 7, 7, 8, 10, 12, 15} is:
A. 7
B. 8
C. 9
D. 10
Rationale: The median is the middle value in an ordered data set. With 7 values (odd number), the
4th value is the median: 8. The mean would be approximately 8.86, but the question asks for the
median.
3. Which of the following is a measure of variability?
A. Mean
B. Mode
C. Standard deviation
D. Median
Rationale: Standard deviation quantifies the spread or dispersion of data around the mean. Mean,
median, and mode are measures of central tendency, not variability.
,4. If P(A) = 0.4 and P(B) = 0.5, and A and B are mutually exclusive, then P(A or B) is:
A. 0.2
B. 0.9
C. 0.1
D. 1.0
Rationale: For mutually exclusive events, P(A or B) = P(A) + P(B) = 0.4 + 0.5 = 0.9. Mutually exclusive
events cannot occur together, so there is no overlap to subtract.
5. A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?
A. 1/6
B. 1/3
C. 1/3
D. 2/3
Rationale: Numbers greater than 4 on a die are 5 and 6, so 2 favorable outcomes out of 6.
Probability = 2/6 = 1/3.
6. The expected value of a discrete random variable X with outcomes {1, 2, 3} and probabilities {0.2,
0.5, 0.3} is:
A. 1.8
, B. 2.1
C. 2.0
D. 2.3
Rationale: E(X) = Σ[x·P(x)] = (1)(0.2) + (2)(0.5) + (3)(0.3) = 0.2 + 1.0 + 0.9 = 2.1.
7. Which distribution is used to model the number of successes in a fixed number of independent
trials with constant probability?
A. Normal distribution
B. Poisson distribution
C. Binomial distribution
D. Exponential distribution
Rationale: The binomial distribution models the number of successes in n independent Bernoulli
trials with success probability p. Poisson models counts over time/space; exponential models time
between events.
8. In a normal distribution with μ = 50 and σ = 10, what is the z-score for X = 65?
A. 0.5
B. 1.5
C. 2.0
QUESTIONS AND CORRECT ANSWERS (PROFESSOR
VERIFIED) | LATEST EDITION | REAL EXAM
Introductory Statistics | Key Domains: Data Collection & Sampling, Descriptive Statistics,
Probability, Random Variables & Distributions, Sampling Distributions, Estimation, Hypothesis
Testing, Correlation & Regression, and Statistical Software Applications | Expert-Aligned Structure |
Exam-Ready Format
Introduction
This structured Math 1280 (Introductory Statistics) Final Exam for 2025 provides a comprehensive
set of high-quality exam-style questions with correct answers and rationales. It emphasizes core
statistical concepts, calculation methods, data interpretation, and proper application of statistical
tests critical for academic and practical success.
Answer Format
All correct answers must appear in bold and cyan blue, accompanied by concise rationales
explaining statistical reasoning, formula application, and why alternative options are
mathematically or conceptually incorrect.
1. A researcher wants to estimate the average height of students at a university. She selects 50
students from a list using a random number generator. This is an example of:
A. Convenience sampling
B. Stratified sampling
C. Simple random sampling
D. Cluster sampling
,Rationale: Simple random sampling involves selecting individuals entirely at random from the
population, where each member has an equal chance of being chosen. Using a random number
generator on a complete list satisfies this condition. Convenience sampling uses readily available
subjects, while stratified and cluster sampling involve dividing the population first.
2. The median of the data set {3, 7, 7, 8, 10, 12, 15} is:
A. 7
B. 8
C. 9
D. 10
Rationale: The median is the middle value in an ordered data set. With 7 values (odd number), the
4th value is the median: 8. The mean would be approximately 8.86, but the question asks for the
median.
3. Which of the following is a measure of variability?
A. Mean
B. Mode
C. Standard deviation
D. Median
Rationale: Standard deviation quantifies the spread or dispersion of data around the mean. Mean,
median, and mode are measures of central tendency, not variability.
,4. If P(A) = 0.4 and P(B) = 0.5, and A and B are mutually exclusive, then P(A or B) is:
A. 0.2
B. 0.9
C. 0.1
D. 1.0
Rationale: For mutually exclusive events, P(A or B) = P(A) + P(B) = 0.4 + 0.5 = 0.9. Mutually exclusive
events cannot occur together, so there is no overlap to subtract.
5. A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?
A. 1/6
B. 1/3
C. 1/3
D. 2/3
Rationale: Numbers greater than 4 on a die are 5 and 6, so 2 favorable outcomes out of 6.
Probability = 2/6 = 1/3.
6. The expected value of a discrete random variable X with outcomes {1, 2, 3} and probabilities {0.2,
0.5, 0.3} is:
A. 1.8
, B. 2.1
C. 2.0
D. 2.3
Rationale: E(X) = Σ[x·P(x)] = (1)(0.2) + (2)(0.5) + (3)(0.3) = 0.2 + 1.0 + 0.9 = 2.1.
7. Which distribution is used to model the number of successes in a fixed number of independent
trials with constant probability?
A. Normal distribution
B. Poisson distribution
C. Binomial distribution
D. Exponential distribution
Rationale: The binomial distribution models the number of successes in n independent Bernoulli
trials with success probability p. Poisson models counts over time/space; exponential models time
between events.
8. In a normal distribution with μ = 50 and σ = 10, what is the z-score for X = 65?
A. 0.5
B. 1.5
C. 2.0
