WGU C955 – Applied probAbility & StAtiStiCS
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Exam: WGU C955 – Applied Probability & Statistics
Question 1:
What is the probability of drawing a red card from a standard deck of 52 playing cards?
1
A) 2
1
B) 4
3
C)
52
1
D) 13
1
Correct Option: A) 2
Rationale:
In a standard deck, there are 26 red cards (hearts and diamonds) out of 52 total cards. The
probability 𝑃of drawing a red card is calculated as:
Number of red cards 26 1
𝑃(red card) = = =
Total number of cards 52 2
Question 2:
Which of the following measures of central tendency is influenced the most by extreme
values?
A) Mean
B) Median
C) Mode
D) Range
Correct Option: A) Mean
Rationale:
The mean is the arithmetic average of a set of values and is calculated by summing all numbers
and dividing by the count. Extreme values (outliers) can significantly skew this value, making it
less representative of the data set as a whole. In contrast, the median is less affected by outliers,
as it represents the middle value when data is sorted.
Question 3:
,In a normal distribution, what percentage of data falls within one standard deviation of the
mean?
A) 50%
B) 68%
C) 95%
D) 99.7%
Correct Option: B) 68%
Rationale:
In a normal distribution, approximately 68% of the data points fall within one standard deviation
from the mean in either direction. This is a key property of normal distributions and is part of the
empirical rule, which describes how data is distributed in terms of standard deviations.
Question 4:
If event A occurs 60% of the time and event B occurs 70% of the time, what is the
probability that both events occur if they are independent?
A) 0.42
B) 0.30
C) 0.60
D) 0.70
Correct Option: A) 0.42
Rationale:
For independent events, the probability that both events occur is the product of their individual
probabilities:
𝑃(𝐴 and 𝐵) = 𝑃(𝐴) × 𝑃(𝐵) = 0.60 × 0.70 = 0.42
Thus, the probability that both events occur is 42%.
Question 5:
Which of the following distributions is used for modeling the number of times an event
occurs in a fixed interval of time or space?
A) Normal distribution
B) Binomial distribution
C) Poisson distribution
D) Uniform distribution
Correct Option: C) Poisson distribution
, Rationale:
The Poisson distribution models the number of events that occur in a fixed interval of time or
space, given that these events happen with a known constant mean rate and are independent of
the time since the last event. This is particularly useful for rare events occurring within a
specified timeframe.
Question 6:
What is the expected value of a discrete random variable?
A) The most common value
B) The average outcome
C) The maximum value
D) The minimum value
Correct Option: B) The average outcome
Rationale:
The expected value (EV) of a discrete random variable provides a measure of the center of its
distribution. It is calculated by summing the products of each possible outcome and its
probability. Essentially, it represents the average value one would expect after many trials.
Question 7:
Which of the following is a property of the standard normal distribution?
A) It has a mean of 1.
B) It is skewed to the right.
C) It has a standard deviation of 1.
D) It has no mode.
Correct Option: C) It has a standard deviation of 1.
Rationale:
The standard normal distribution is a special case of the normal distribution where the mean is 0
and the standard deviation is 1. This allows for the use of Z-scores to calculate probabilities and
percentiles more easily.
Question 8:
In hypothesis testing, what is the null hypothesis typically denoted as?
A) H1
B) H0
StUdy GUide 2026 | objeCtive ASSeSSment (oA)
exAm prep, prACtiCe QUeStionS, Step-by-Step
StAtiStiCAl SolUtionS, verified AnSWerS & dAtA
AnAlySiS mAStery reSoUrCe
Exam: WGU C955 – Applied Probability & Statistics
Question 1:
What is the probability of drawing a red card from a standard deck of 52 playing cards?
1
A) 2
1
B) 4
3
C)
52
1
D) 13
1
Correct Option: A) 2
Rationale:
In a standard deck, there are 26 red cards (hearts and diamonds) out of 52 total cards. The
probability 𝑃of drawing a red card is calculated as:
Number of red cards 26 1
𝑃(red card) = = =
Total number of cards 52 2
Question 2:
Which of the following measures of central tendency is influenced the most by extreme
values?
A) Mean
B) Median
C) Mode
D) Range
Correct Option: A) Mean
Rationale:
The mean is the arithmetic average of a set of values and is calculated by summing all numbers
and dividing by the count. Extreme values (outliers) can significantly skew this value, making it
less representative of the data set as a whole. In contrast, the median is less affected by outliers,
as it represents the middle value when data is sorted.
Question 3:
,In a normal distribution, what percentage of data falls within one standard deviation of the
mean?
A) 50%
B) 68%
C) 95%
D) 99.7%
Correct Option: B) 68%
Rationale:
In a normal distribution, approximately 68% of the data points fall within one standard deviation
from the mean in either direction. This is a key property of normal distributions and is part of the
empirical rule, which describes how data is distributed in terms of standard deviations.
Question 4:
If event A occurs 60% of the time and event B occurs 70% of the time, what is the
probability that both events occur if they are independent?
A) 0.42
B) 0.30
C) 0.60
D) 0.70
Correct Option: A) 0.42
Rationale:
For independent events, the probability that both events occur is the product of their individual
probabilities:
𝑃(𝐴 and 𝐵) = 𝑃(𝐴) × 𝑃(𝐵) = 0.60 × 0.70 = 0.42
Thus, the probability that both events occur is 42%.
Question 5:
Which of the following distributions is used for modeling the number of times an event
occurs in a fixed interval of time or space?
A) Normal distribution
B) Binomial distribution
C) Poisson distribution
D) Uniform distribution
Correct Option: C) Poisson distribution
, Rationale:
The Poisson distribution models the number of events that occur in a fixed interval of time or
space, given that these events happen with a known constant mean rate and are independent of
the time since the last event. This is particularly useful for rare events occurring within a
specified timeframe.
Question 6:
What is the expected value of a discrete random variable?
A) The most common value
B) The average outcome
C) The maximum value
D) The minimum value
Correct Option: B) The average outcome
Rationale:
The expected value (EV) of a discrete random variable provides a measure of the center of its
distribution. It is calculated by summing the products of each possible outcome and its
probability. Essentially, it represents the average value one would expect after many trials.
Question 7:
Which of the following is a property of the standard normal distribution?
A) It has a mean of 1.
B) It is skewed to the right.
C) It has a standard deviation of 1.
D) It has no mode.
Correct Option: C) It has a standard deviation of 1.
Rationale:
The standard normal distribution is a special case of the normal distribution where the mean is 0
and the standard deviation is 1. This allows for the use of Z-scores to calculate probabilities and
percentiles more easily.
Question 8:
In hypothesis testing, what is the null hypothesis typically denoted as?
A) H1
B) H0
