CALIFORNIA – STATISTICS FOR BUSINESS & ECONOMICS – COMPREHENSIVE FINAL EXAM
REVIEW & SOLVED PROBLEMS – 2026/2027 – QUESTIONS AND ANSWERS | VERIFIED AND
WELL DETAILED ANSWERS | PLUS RATIONALES | GUARANTEED PASS | LATEST EXAM
UPDATE
CORE DOMAINS
Descriptive Statistics and Data Visualization
Probability Theory and Probability Distributions
Sampling Distributions and the Central Limit Theorem
Confidence Interval Estimation
Hypothesis Testing for One and Two Populations
Analysis of Variance and Experimental Design
Simple and Multiple Linear Regression
Chi-Square Tests and Nonparametric Methods
Time Series Analysis and Index Numbers
Statistical Decision Theory and Business Ethics
INTRODUCTION
This comprehensive final examination assesses mastery of statistical methods applied to business
and economic decision-making. It evaluates foundational theory, quantitative reasoning, and the
interpretation of statistical evidence. The exam comprises multiple-choice and scenario-based
questions that require application, analysis, and professional judgment. Emphasis is placed on
real-world workplace contexts, ethical practice, regulatory compliance, and data-driven decision-
making. Candidates must demonstrate competency in probability, inference, regression, and
experimental design while selecting defensible conclusions from quantitative output. The
assessment prepares professionals to communicate statistical findings accurately and to uphold
standards of integrity in business analytics.
SECTION ONE – QUESTIONS 1–100
Question 1
A retail chain collects the number of daily customer complaints over 30 days. Which measure
of central tendency is most appropriate for summarizing the typical number of complaints
when the data contain two extreme outliers?
,A. Mean
B. Median
C. Mode
D. Geometric mean
🟢 Correct answer: B
🔴 Explanation: The median is resistant to extreme values, whereas the mean is strongly
influenced by outliers. For skewed data with outliers, the median better represents the typical
value.
Question 2
A financial analyst calculates the coefficient of variation for two investment portfolios. Portfolio
X has a mean return of 12% and a standard deviation of 3%. Portfolio Y has a mean return of
20% and a standard deviation of 4%. Which portfolio has greater relative variability?
A. Portfolio X, because its standard deviation is smaller
B. Portfolio Y, because its mean return is larger
C. Portfolio X, because its coefficient of variation is 0.25
D. Portfolio Y, because its coefficient of variation is 0.20
🟢 Correct answer: C
🔴 Explanation: CV = standard deviation divided by mean. Portfolio X CV = 3/12 = 0.25.
Portfolio Y CV = 4/20 = 0.20. Portfolio X has greater relative variability.
Question 3
In a positively skewed distribution, which relationship among the mean, median, and mode
typically holds?
A. Mean = Median = Mode
B. Mean < Median < Mode
C. Mode < Median < Mean
D. Median < Mode < Mean
🟢 Correct answer: C
🔴 Explanation: In a positively skewed distribution the long tail is to the right, pulling the mean
above the median, and the mode is the smallest of the three measures.
,Question 4
A quality control manager wants to display the proportion of defective units by defect
category. Which graphical display is most appropriate?
A. Histogram
B. Scatter plot
C. Pareto chart
D. Stem-and-leaf plot
🟢 Correct answer: C
🔴 Explanation: A Pareto chart is a bar chart ordered by frequency and is used to display
categorical defect counts or proportions, highlighting the most significant categories.
Question 5
An economist reports that the probability of a recession is 0.30, and the probability of a stock
market decline given a recession is 0.80. What is the probability of both a recession and a
market decline?
A. 0.24
B. 0.30
C. 0.50
D. 0.80
🟢 Correct answer: A
🔴 Explanation: Using the multiplication rule, P(A and B) = P(A) × P(B|A) = 0.30 × 0.80 = 0.24.
Question 6
Two events A and B are mutually exclusive. If P(A) = 0.40 and P(B) = 0.35, what is P(A or B)?
A. 0.14
B. 0.60
C. 0.75
D. 1.00
🟢 Correct answer: C
🔴 Explanation: For mutually exclusive events, P(A or B) = P(A) + P(B) = 0.40 + 0.35 = 0.75.
, Question 7
A company’s sales team has 60% male and 40% female employees. Among males, 30% exceed
quota; among females, 45% exceed quota. If an employee exceeded quota, what is the
probability the employee is female?
A. 0.18
B. 0.40
C. 0.50
D. 0.72
🟢 Correct answer: C
🔴 Explanation: P(F|E) = [P(F) × P(E|F)] / [P(M) × P(E|M) + P(F) × P(E|F)] = (0.40 × 0.45) / (0.60 ×
0.30 + 0.40 × 0.45) = 0..36 = 0.50.
Question 8
A discrete random variable X has the following distribution: P(X=0)=0.2, P(X=1)=0.5,
P(X=2)=0.3. What is the expected value of X?
A. 0.8
B. 1.0
C. 1.1
D. 1.5
🟢 Correct answer: C
🔴 Explanation: E(X) = 0(0.2) + 1(0.5) + 2(0.3) = 0 + 0.5 + 0.6 = 1.1.
Question 9
In a binomial distribution with n = 20 and p = 0.25, what is the mean?
A. 4
B. 5
C. 10
D. 15
🟢 Correct answer: B
🔴 Explanation: The mean of a binomial distribution is np = 20 × 0.25 = 5.
REVIEW & SOLVED PROBLEMS – 2026/2027 – QUESTIONS AND ANSWERS | VERIFIED AND
WELL DETAILED ANSWERS | PLUS RATIONALES | GUARANTEED PASS | LATEST EXAM
UPDATE
CORE DOMAINS
Descriptive Statistics and Data Visualization
Probability Theory and Probability Distributions
Sampling Distributions and the Central Limit Theorem
Confidence Interval Estimation
Hypothesis Testing for One and Two Populations
Analysis of Variance and Experimental Design
Simple and Multiple Linear Regression
Chi-Square Tests and Nonparametric Methods
Time Series Analysis and Index Numbers
Statistical Decision Theory and Business Ethics
INTRODUCTION
This comprehensive final examination assesses mastery of statistical methods applied to business
and economic decision-making. It evaluates foundational theory, quantitative reasoning, and the
interpretation of statistical evidence. The exam comprises multiple-choice and scenario-based
questions that require application, analysis, and professional judgment. Emphasis is placed on
real-world workplace contexts, ethical practice, regulatory compliance, and data-driven decision-
making. Candidates must demonstrate competency in probability, inference, regression, and
experimental design while selecting defensible conclusions from quantitative output. The
assessment prepares professionals to communicate statistical findings accurately and to uphold
standards of integrity in business analytics.
SECTION ONE – QUESTIONS 1–100
Question 1
A retail chain collects the number of daily customer complaints over 30 days. Which measure
of central tendency is most appropriate for summarizing the typical number of complaints
when the data contain two extreme outliers?
,A. Mean
B. Median
C. Mode
D. Geometric mean
🟢 Correct answer: B
🔴 Explanation: The median is resistant to extreme values, whereas the mean is strongly
influenced by outliers. For skewed data with outliers, the median better represents the typical
value.
Question 2
A financial analyst calculates the coefficient of variation for two investment portfolios. Portfolio
X has a mean return of 12% and a standard deviation of 3%. Portfolio Y has a mean return of
20% and a standard deviation of 4%. Which portfolio has greater relative variability?
A. Portfolio X, because its standard deviation is smaller
B. Portfolio Y, because its mean return is larger
C. Portfolio X, because its coefficient of variation is 0.25
D. Portfolio Y, because its coefficient of variation is 0.20
🟢 Correct answer: C
🔴 Explanation: CV = standard deviation divided by mean. Portfolio X CV = 3/12 = 0.25.
Portfolio Y CV = 4/20 = 0.20. Portfolio X has greater relative variability.
Question 3
In a positively skewed distribution, which relationship among the mean, median, and mode
typically holds?
A. Mean = Median = Mode
B. Mean < Median < Mode
C. Mode < Median < Mean
D. Median < Mode < Mean
🟢 Correct answer: C
🔴 Explanation: In a positively skewed distribution the long tail is to the right, pulling the mean
above the median, and the mode is the smallest of the three measures.
,Question 4
A quality control manager wants to display the proportion of defective units by defect
category. Which graphical display is most appropriate?
A. Histogram
B. Scatter plot
C. Pareto chart
D. Stem-and-leaf plot
🟢 Correct answer: C
🔴 Explanation: A Pareto chart is a bar chart ordered by frequency and is used to display
categorical defect counts or proportions, highlighting the most significant categories.
Question 5
An economist reports that the probability of a recession is 0.30, and the probability of a stock
market decline given a recession is 0.80. What is the probability of both a recession and a
market decline?
A. 0.24
B. 0.30
C. 0.50
D. 0.80
🟢 Correct answer: A
🔴 Explanation: Using the multiplication rule, P(A and B) = P(A) × P(B|A) = 0.30 × 0.80 = 0.24.
Question 6
Two events A and B are mutually exclusive. If P(A) = 0.40 and P(B) = 0.35, what is P(A or B)?
A. 0.14
B. 0.60
C. 0.75
D. 1.00
🟢 Correct answer: C
🔴 Explanation: For mutually exclusive events, P(A or B) = P(A) + P(B) = 0.40 + 0.35 = 0.75.
, Question 7
A company’s sales team has 60% male and 40% female employees. Among males, 30% exceed
quota; among females, 45% exceed quota. If an employee exceeded quota, what is the
probability the employee is female?
A. 0.18
B. 0.40
C. 0.50
D. 0.72
🟢 Correct answer: C
🔴 Explanation: P(F|E) = [P(F) × P(E|F)] / [P(M) × P(E|M) + P(F) × P(E|F)] = (0.40 × 0.45) / (0.60 ×
0.30 + 0.40 × 0.45) = 0..36 = 0.50.
Question 8
A discrete random variable X has the following distribution: P(X=0)=0.2, P(X=1)=0.5,
P(X=2)=0.3. What is the expected value of X?
A. 0.8
B. 1.0
C. 1.1
D. 1.5
🟢 Correct answer: C
🔴 Explanation: E(X) = 0(0.2) + 1(0.5) + 2(0.3) = 0 + 0.5 + 0.6 = 1.1.
Question 9
In a binomial distribution with n = 20 and p = 0.25, what is the mean?
A. 4
B. 5
C. 10
D. 15
🟢 Correct answer: B
🔴 Explanation: The mean of a binomial distribution is np = 20 × 0.25 = 5.
