,WGU C955 Applied Probability and Statistics Final
Exam | 2026/2027 Edition (PDF)
1. Which of the following best describes the set of numbers that includes all positive counting numbers,
their negatives, and zero?
A) Whole numbers
B) Integers
C) Rational numbers
D) Real numbers
Correct Answer: Integers
Rationale: Integers are defined as the set of whole numbers and their opposites, including zero, negative
numbers, and positive numbers without fractions or decimals. Whole numbers exclude negatives,
rational numbers include fractions, and real numbers include irrational values, making integers the most
precise choice.
2. What is the primary characteristic of discrete data?
A) It can take any value within a range
B) It has distinct, countable values with unconnected points
C) It is measured on a continuous scale
D) It always represents categorical information
Correct Answer: It has distinct, countable values with unconnected points
Rationale: Discrete data consists of distinct values that can be counted, often visualized as unconnected
points like dots on a graph. Continuous data takes any value within a range, and discrete data can be
numerical, not just categorical, making the countable distinction the defining feature.
3. According to the order of operations (PEMDAS), which operation should be performed first in the
expression 8 + 2 × (6 − 4) ÷ 2?
,A) Addition
B) Subtraction
C) Multiplication
D) Division
Correct Answer: Subtraction
Rationale: PEMDAS dictates that operations inside parentheses are completed first. In this expression,
the parentheses contain 6 − 4, so subtraction is the initial operation, followed by multiplication and
division from left to right, then addition last.
4. What is the simplified result of 3(2x + 4) − 5x?
A) x + 12
B) 11x + 12
C) x + 4
D) 6x + 7
Correct Answer: x + 12
Rationale: Applying the distributive property gives 6x + 12 − 5x. Combining like terms (6x − 5x) yields x +
12. The other options result from incorrect distribution or combining unlike terms, such as adding
coefficients incorrectly.
5. In a normal distribution, what percentage of data falls within one standard deviation of the mean?
A) 68%
B) 95%
C) 99.7%
D) 50%
Correct Answer: 68%
, Rationale: The Empirical Rule for normal distributions states that approximately 68% of data lies within
±1 standard deviation from the mean. Two standard deviations cover about 95%, and three cover about
99.7%, making 68% the correct percentage for one standard deviation.
6. A researcher is studying the relationship between two variables and creates a scatterplot. Which
statistic measures the strength and direction of a linear relationship?
A) Standard deviation
B) Mean
C) Correlation coefficient
D) Slope
Correct Answer: Correlation coefficient
Rationale: The correlation coefficient (r) quantifies both the strength and direction of a linear association
between two variables, ranging from -1 to +1. Standard deviation measures spread, mean measures
center, and slope indicates rate of change but not overall strength.
7. Which term refers to a variable that is not included in an analysis but is related to two other
associated variables, potentially creating a false impression of causation?
A) Independent variable
B) Confounding variable
C) Lurking variable
D) Response variable
Correct Answer: Lurking variable
Rationale: A lurking variable is excluded from analysis but influences both variables under study,
potentially creating a spurious association. Confounding variables are similar but typically accounted for
in design; lurking variables remain unobserved, making them the correct term here.
8. What is the median of the dataset: 3, 7, 7, 10, 12?
Exam | 2026/2027 Edition (PDF)
1. Which of the following best describes the set of numbers that includes all positive counting numbers,
their negatives, and zero?
A) Whole numbers
B) Integers
C) Rational numbers
D) Real numbers
Correct Answer: Integers
Rationale: Integers are defined as the set of whole numbers and their opposites, including zero, negative
numbers, and positive numbers without fractions or decimals. Whole numbers exclude negatives,
rational numbers include fractions, and real numbers include irrational values, making integers the most
precise choice.
2. What is the primary characteristic of discrete data?
A) It can take any value within a range
B) It has distinct, countable values with unconnected points
C) It is measured on a continuous scale
D) It always represents categorical information
Correct Answer: It has distinct, countable values with unconnected points
Rationale: Discrete data consists of distinct values that can be counted, often visualized as unconnected
points like dots on a graph. Continuous data takes any value within a range, and discrete data can be
numerical, not just categorical, making the countable distinction the defining feature.
3. According to the order of operations (PEMDAS), which operation should be performed first in the
expression 8 + 2 × (6 − 4) ÷ 2?
,A) Addition
B) Subtraction
C) Multiplication
D) Division
Correct Answer: Subtraction
Rationale: PEMDAS dictates that operations inside parentheses are completed first. In this expression,
the parentheses contain 6 − 4, so subtraction is the initial operation, followed by multiplication and
division from left to right, then addition last.
4. What is the simplified result of 3(2x + 4) − 5x?
A) x + 12
B) 11x + 12
C) x + 4
D) 6x + 7
Correct Answer: x + 12
Rationale: Applying the distributive property gives 6x + 12 − 5x. Combining like terms (6x − 5x) yields x +
12. The other options result from incorrect distribution or combining unlike terms, such as adding
coefficients incorrectly.
5. In a normal distribution, what percentage of data falls within one standard deviation of the mean?
A) 68%
B) 95%
C) 99.7%
D) 50%
Correct Answer: 68%
, Rationale: The Empirical Rule for normal distributions states that approximately 68% of data lies within
±1 standard deviation from the mean. Two standard deviations cover about 95%, and three cover about
99.7%, making 68% the correct percentage for one standard deviation.
6. A researcher is studying the relationship between two variables and creates a scatterplot. Which
statistic measures the strength and direction of a linear relationship?
A) Standard deviation
B) Mean
C) Correlation coefficient
D) Slope
Correct Answer: Correlation coefficient
Rationale: The correlation coefficient (r) quantifies both the strength and direction of a linear association
between two variables, ranging from -1 to +1. Standard deviation measures spread, mean measures
center, and slope indicates rate of change but not overall strength.
7. Which term refers to a variable that is not included in an analysis but is related to two other
associated variables, potentially creating a false impression of causation?
A) Independent variable
B) Confounding variable
C) Lurking variable
D) Response variable
Correct Answer: Lurking variable
Rationale: A lurking variable is excluded from analysis but influences both variables under study,
potentially creating a spurious association. Confounding variables are similar but typically accounted for
in design; lurking variables remain unobserved, making them the correct term here.
8. What is the median of the dataset: 3, 7, 7, 10, 12?
