1|Page
WGU C955 Applied Probability and Statistics 2026-2027 BANK
QUESTIONS WITH DETAILED VERIFIED ANSWERS EXAM
QUESTIONS WILL COME FROM HERE (100% CORRECT
ANSWERS A+ GRADED
1. A researcher is studying the relationship between hours of sleep and
exam performance. Which type of study is this if the researcher only
observes and records data without intervening?
A) Experimental study
B) Observational study
C) Simulation study
D) Survey study
Answer: B
Explanation: In an observational study, the researcher measures
variables of interest without attempting to influence the responses.
Here, the researcher is merely recording sleep hours and exam scores,
making no intervention, which defines an observational study.
2. A pharmaceutical company gives one group a new drug and another
group a placebo to compare blood pressure outcomes. What type of
study is this?
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A) Observational study
B) Retrospective study
C) Experimental study
D) Correlational study
Answer: C
Explanation: An experimental study involves the deliberate
manipulation of one variable (the treatment) to observe its effect on
another variable. The imposition of a drug versus a placebo constitutes
a controlled experiment.
3. In a data set, the value that appears most frequently is known as the:
A) Mean
B) Median
C) Mode
D) Range
Answer: C
Explanation: The mode is the measure of central tendency that
identifies the most frequently occurring value in a data set. The mean is
the arithmetic average, and the median is the middle value when data
are ordered.
4. A student's score is at the 80th percentile on a standardized test. This
means:
A) The student answered 80% of the questions correctly
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B) The student scored higher than 80% of the test-takers
C) The student is in the top 20% of the class by grade point average
D) The student needs to improve by 20% to pass
Answer: B
Explanation: The kth percentile is a value below which k percent of the
observations fall. Being at the 80th percentile implies the student
performed as well as or better than 80% of the reference group.
5. Which of the following describes a discrete random variable?
A) The height of a tree
B) The number of cars in a parking lot
C) The time it takes to run a marathon
D) The weight of a parcel
Answer: B
Explanation: A discrete variable can take on a countable number of
values. The number of cars is a count and thus a discrete variable.
Height, time, and weight are continuous variables, as they can take any
value within an interval.
6. The sum of all probabilities in a discrete probability distribution must
equal:
A) 0
B) 1
C) 100
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D) It depends on the number of outcomes
Answer: B
Explanation: By the axioms of probability, the probability that a random
variable takes some value within its sample space is 1. For a discrete
probability distribution, the sum of P(X=x) over all possible x is exactly
1.
7. Two events are said to be mutually exclusive if:
A) They cannot occur at the same time
B) One causes the other to occur
C) They have the same probability
D) They are independent
Answer: A
Explanation: Mutually exclusive events have no outcomes in common,
meaning the occurrence of one precludes the occurrence of the other.
For example, a coin toss cannot result in both heads and tails
simultaneously.
8. If P(A) = 0.4 and P(B) = 0.3, and A and B are mutually exclusive, what
is P(A or B)?
A) 0.12
B) 0.58
C) 0.70
D) 1.0
WGU C955 Applied Probability and Statistics 2026-2027 BANK
QUESTIONS WITH DETAILED VERIFIED ANSWERS EXAM
QUESTIONS WILL COME FROM HERE (100% CORRECT
ANSWERS A+ GRADED
1. A researcher is studying the relationship between hours of sleep and
exam performance. Which type of study is this if the researcher only
observes and records data without intervening?
A) Experimental study
B) Observational study
C) Simulation study
D) Survey study
Answer: B
Explanation: In an observational study, the researcher measures
variables of interest without attempting to influence the responses.
Here, the researcher is merely recording sleep hours and exam scores,
making no intervention, which defines an observational study.
2. A pharmaceutical company gives one group a new drug and another
group a placebo to compare blood pressure outcomes. What type of
study is this?
,2|Page
A) Observational study
B) Retrospective study
C) Experimental study
D) Correlational study
Answer: C
Explanation: An experimental study involves the deliberate
manipulation of one variable (the treatment) to observe its effect on
another variable. The imposition of a drug versus a placebo constitutes
a controlled experiment.
3. In a data set, the value that appears most frequently is known as the:
A) Mean
B) Median
C) Mode
D) Range
Answer: C
Explanation: The mode is the measure of central tendency that
identifies the most frequently occurring value in a data set. The mean is
the arithmetic average, and the median is the middle value when data
are ordered.
4. A student's score is at the 80th percentile on a standardized test. This
means:
A) The student answered 80% of the questions correctly
,3|Page
B) The student scored higher than 80% of the test-takers
C) The student is in the top 20% of the class by grade point average
D) The student needs to improve by 20% to pass
Answer: B
Explanation: The kth percentile is a value below which k percent of the
observations fall. Being at the 80th percentile implies the student
performed as well as or better than 80% of the reference group.
5. Which of the following describes a discrete random variable?
A) The height of a tree
B) The number of cars in a parking lot
C) The time it takes to run a marathon
D) The weight of a parcel
Answer: B
Explanation: A discrete variable can take on a countable number of
values. The number of cars is a count and thus a discrete variable.
Height, time, and weight are continuous variables, as they can take any
value within an interval.
6. The sum of all probabilities in a discrete probability distribution must
equal:
A) 0
B) 1
C) 100
, 4|Page
D) It depends on the number of outcomes
Answer: B
Explanation: By the axioms of probability, the probability that a random
variable takes some value within its sample space is 1. For a discrete
probability distribution, the sum of P(X=x) over all possible x is exactly
1.
7. Two events are said to be mutually exclusive if:
A) They cannot occur at the same time
B) One causes the other to occur
C) They have the same probability
D) They are independent
Answer: A
Explanation: Mutually exclusive events have no outcomes in common,
meaning the occurrence of one precludes the occurrence of the other.
For example, a coin toss cannot result in both heads and tails
simultaneously.
8. If P(A) = 0.4 and P(B) = 0.3, and A and B are mutually exclusive, what
is P(A or B)?
A) 0.12
B) 0.58
C) 0.70
D) 1.0
