WGU C955 APPLIED PROBABILITY AND STATISTICS FINAL EXAM STUDY GUIDE |
TESTBANK | PRACTICE QUESTIONS & ANSWERS | EXAM PREPARATION |
COMPREHENSIVE PRACTICE EXAM | LATEST UPDATE 2026/2027
Examiner:
Western Governors University (WGU)
TABLE OF CONTENTS
1. Descriptive Statistics
2. Data Visualization and Interpretation
3. Probability Concepts
4. Counting Principles
5. Conditional Probability and Independence
6. Random Variables and Probability Distributions
7. Expected Value and Variance
8. Sampling Distributions
9. Confidence Intervals
10. Hypothesis Testing
11. Correlation and Linear Regression
12. Statistical Modeling and Interpretation
13. Decision-Making Using Statistical Evidence
14. Applied Statistical Reasoning
DESCRIPTIVE STATISTICS || DATA ANALYSIS || FREQUENCY DISTRIBUTIONS ||
PROBABILITY || COUNTING PRINCIPLES || CONDITIONAL PROBABILITY ||
BINOMIAL DISTRIBUTION || NORMAL DISTRIBUTION || SAMPLING
DISTRIBUTIONS || CENTRAL LIMIT THEOREM || CONFIDENCE INTERVALS ||
HYPOTHESIS TESTING || P-VALUES || TYPE I ERROR || TYPE II ERROR ||
CORRELATION || LINEAR REGRESSION || EXPECTED VALUE || VARIANCE ||
STANDARD DEVIATION || RANDOM VARIABLES || STATISTICAL INFERENCE ||
DECISION ANALYSIS || CRITICAL THINKING || APPLIED STATISTICS
,QUESTION 1.
A manufacturing process produces components with a historical defect rate of 4%.
An inspector randomly selects five components. Assuming independence, what is the
probability that exactly one component is defective?
A. 5(0.04)(0.96)4
B. (0.04)5
C. 1 − (0.96)5
D. 5(0.96)(0.04)4
🔴 Correct Answer: A. 5(0.04)(0.96)4
🔵 Explanation: This is a binomial probability with n = 5, x = 1, and p = 0.04. The
5
probability equals (1)(0.04)1 (0.96)4 . The remaining options either compute a
different event or misuse the binomial formula.
QUESTION 2.
A researcher compares two data sets. Dataset A has a mean of 50 and standard
deviation of 5. Dataset B has a mean of 200 and standard deviation of 20. Which
statement is most accurate?
A. Dataset B is more variable because its standard deviation is larger.
B. Both datasets have equal relative variability.
C. Dataset A has greater relative variability.
D. Relative variability cannot be compared.
🔴 Correct Answer: B. Both datasets have equal relative variability.
🔵 Explanation: Relative variability is measured using the coefficient of variation.
Dataset A has 5/50 = 0.10, while Dataset B has 20/200 = 0.10. Although Dataset B has
,a larger standard deviation, both datasets exhibit identical variability relative to their
means.
QUESTION 3.
An event A has probability 0.55, event B has probability 0.30, and P(A ∩ B)=0.15.
What is P(A ∪ B)?
A. 0.70
B. 0.85
C. 0.40
D. 1.00
🔴 Correct Answer: A. 0.70
🔵 Explanation: Apply the addition rule: P(A ∪ B)=P(A)+P(B)-P(A ∩ B)=0.55+0.30-
0.15=0.70. The other answers result from incorrect application of the addition rule.
QUESTION 4.
A distribution is strongly right-skewed with several unusually large observations.
Which measure of center is generally most appropriate?
A. Midrange
B. Mean
C. Median
D. Maximum
🔴 Correct Answer: C. Median
🔵 Explanation: The median is resistant to extreme observations and better represents
the center of a skewed distribution. The mean is influenced by outliers, while the
, midrange and maximum are even more sensitive.
QUESTION 5.
Which statement best describes mutually exclusive events?
A. They cannot occur together.
B. They always have equal probability.
C. They are always independent.
D. Their probabilities always sum to one.
🔴 Correct Answer: A. They cannot occur together.
🔵 Explanation: Mutually exclusive events share no common outcomes, so their
intersection is zero. They need not have equal probabilities, are generally not
independent unless one has probability zero, and their probabilities do not necessarily
sum to one.
QUESTION 6.
A confidence interval for a population mean is reported as (42.1, 47.9). Which
interpretation is correct?
A. Ninety-five percent of observations fall inside the interval.
B. The sample mean has a 95% probability of lying inside the interval.
C. The procedure used to create the interval captures the true mean in about 95% of
repeated samples.
D. The population mean changes from sample to sample.
🔴 Correct Answer: C. The procedure used to create the interval captures the true
mean in about 95% of repeated samples.
TESTBANK | PRACTICE QUESTIONS & ANSWERS | EXAM PREPARATION |
COMPREHENSIVE PRACTICE EXAM | LATEST UPDATE 2026/2027
Examiner:
Western Governors University (WGU)
TABLE OF CONTENTS
1. Descriptive Statistics
2. Data Visualization and Interpretation
3. Probability Concepts
4. Counting Principles
5. Conditional Probability and Independence
6. Random Variables and Probability Distributions
7. Expected Value and Variance
8. Sampling Distributions
9. Confidence Intervals
10. Hypothesis Testing
11. Correlation and Linear Regression
12. Statistical Modeling and Interpretation
13. Decision-Making Using Statistical Evidence
14. Applied Statistical Reasoning
DESCRIPTIVE STATISTICS || DATA ANALYSIS || FREQUENCY DISTRIBUTIONS ||
PROBABILITY || COUNTING PRINCIPLES || CONDITIONAL PROBABILITY ||
BINOMIAL DISTRIBUTION || NORMAL DISTRIBUTION || SAMPLING
DISTRIBUTIONS || CENTRAL LIMIT THEOREM || CONFIDENCE INTERVALS ||
HYPOTHESIS TESTING || P-VALUES || TYPE I ERROR || TYPE II ERROR ||
CORRELATION || LINEAR REGRESSION || EXPECTED VALUE || VARIANCE ||
STANDARD DEVIATION || RANDOM VARIABLES || STATISTICAL INFERENCE ||
DECISION ANALYSIS || CRITICAL THINKING || APPLIED STATISTICS
,QUESTION 1.
A manufacturing process produces components with a historical defect rate of 4%.
An inspector randomly selects five components. Assuming independence, what is the
probability that exactly one component is defective?
A. 5(0.04)(0.96)4
B. (0.04)5
C. 1 − (0.96)5
D. 5(0.96)(0.04)4
🔴 Correct Answer: A. 5(0.04)(0.96)4
🔵 Explanation: This is a binomial probability with n = 5, x = 1, and p = 0.04. The
5
probability equals (1)(0.04)1 (0.96)4 . The remaining options either compute a
different event or misuse the binomial formula.
QUESTION 2.
A researcher compares two data sets. Dataset A has a mean of 50 and standard
deviation of 5. Dataset B has a mean of 200 and standard deviation of 20. Which
statement is most accurate?
A. Dataset B is more variable because its standard deviation is larger.
B. Both datasets have equal relative variability.
C. Dataset A has greater relative variability.
D. Relative variability cannot be compared.
🔴 Correct Answer: B. Both datasets have equal relative variability.
🔵 Explanation: Relative variability is measured using the coefficient of variation.
Dataset A has 5/50 = 0.10, while Dataset B has 20/200 = 0.10. Although Dataset B has
,a larger standard deviation, both datasets exhibit identical variability relative to their
means.
QUESTION 3.
An event A has probability 0.55, event B has probability 0.30, and P(A ∩ B)=0.15.
What is P(A ∪ B)?
A. 0.70
B. 0.85
C. 0.40
D. 1.00
🔴 Correct Answer: A. 0.70
🔵 Explanation: Apply the addition rule: P(A ∪ B)=P(A)+P(B)-P(A ∩ B)=0.55+0.30-
0.15=0.70. The other answers result from incorrect application of the addition rule.
QUESTION 4.
A distribution is strongly right-skewed with several unusually large observations.
Which measure of center is generally most appropriate?
A. Midrange
B. Mean
C. Median
D. Maximum
🔴 Correct Answer: C. Median
🔵 Explanation: The median is resistant to extreme observations and better represents
the center of a skewed distribution. The mean is influenced by outliers, while the
, midrange and maximum are even more sensitive.
QUESTION 5.
Which statement best describes mutually exclusive events?
A. They cannot occur together.
B. They always have equal probability.
C. They are always independent.
D. Their probabilities always sum to one.
🔴 Correct Answer: A. They cannot occur together.
🔵 Explanation: Mutually exclusive events share no common outcomes, so their
intersection is zero. They need not have equal probabilities, are generally not
independent unless one has probability zero, and their probabilities do not necessarily
sum to one.
QUESTION 6.
A confidence interval for a population mean is reported as (42.1, 47.9). Which
interpretation is correct?
A. Ninety-five percent of observations fall inside the interval.
B. The sample mean has a 95% probability of lying inside the interval.
C. The procedure used to create the interval captures the true mean in about 95% of
repeated samples.
D. The population mean changes from sample to sample.
🔴 Correct Answer: C. The procedure used to create the interval captures the true
mean in about 95% of repeated samples.
