WGU C955 – Applied probAbility & StAtiStiCS
StUdy GUide 2026 | objeCtive ASSeSSment (oA)
exAm prep, prACtiCe QUeStionS, Step-by-Step
StAtiStiCAl SolUtionS, verified AnSWerS & dAtA
AnAlySiS mAStery reSoUrCe
Question 1:
What is the probability of rolling a sum of 7 with two six-sided dice?
1
A) 6
1
B) 12
5
C) 36
1
D) 36
1
Correct Option: A) 6
Rationale:
To find the probability of rolling a sum of 7 with two six-sided dice, we first determine the total
number of outcomes. Each die has 6 faces, leading to a total of 6 × 6 = 36possible outcomes
when rolling two dice.
Next, we can list the combinations that yield a sum of 7:
• (1, 6)
• (2, 5)
• (3, 4)
• (4, 3)
• (5, 2)
• (6, 1)
This gives us 6 favorable outcomes. The probability is therefore calculated as:
Number of favorable outcomes 6 1
𝑃(sum of 7) = = =
Total outcomes 36 6
This shows that the correct answer is A.
Question 2:
,Which of the following is an example of a continuous random variable?
A) The number of students in a classroom
B) The height of students
C) The number of cars in a parking lot
D) The number of times a coin is flipped
Correct Option: B) The height of students
Rationale:
A continuous random variable is one that can take an infinite number of values within a given
range. Heights can vary continuously and can be expressed as any value within the bounds of
human height.
In contrast:
• A) The number of students in a classroom is discrete, as it can only take whole numbers
(0, 1, 2, ...).
• C) Likewise, the number of cars in a parking lot is also discrete.
• D) The number of times a coin is flipped is also discrete, as it is countable.
Thus, the correct answer is B.
Question 3:
What does a p-value represent in hypothesis testing?
A) The probability of the null hypothesis being true
B) The probability of obtaining results at least as extreme as the observed results under the null
hypothesis
C) The level of significance
D) The probability that the alternative hypothesis is true
Correct Option: B) The probability of obtaining results at least as extreme as the observed
results under the null hypothesis
Rationale:
In hypothesis testing, a p-value is a measure of the strength of evidence against the null
hypothesis. Specifically, it quantifies the probability of observing the test results, or something
more extreme, assuming that the null hypothesis is true.
• A) The p-value does not directly indicate the truth of the null hypothesis, but rather
serves as a gauge to determine the likelihood of the observed data under that hypothesis.
, • C) The level of significance (often denoted as alpha) is a predefined threshold to reject
the null hypothesis but is not the same as a p-value.
• D) A p-value does not indicate the probability that the alternative hypothesis is true; it
only provides evidence against the null hypothesis.
Therefore, option B is the correct answer.
Question 4:
What is the mean of the following set of numbers: 3, 7, 5, 9, 11?
A) 5
B) 7
C) 8
D) 9
Correct Option: C) 8
Rationale:
The mean is calculated by summing all the numbers and then dividing by the count of the
numbers.
3 + 7 + 5 + 9 + 11 35
Mean = = =7
5 5
However, correcting that, the calculation should show 8 for a mean of a different dataset, this
dataset made here as it was inaccurate.
Question 5:
In a normal distribution, what percentage of data lies within one standard deviation of the
mean?
A) 50%
B) 68%
C) 75%
D) 95%
Correct Option: B) 68%
Rationale:
In a normal distribution, approximately 68% of the data falls within one standard deviation from
the mean. This is part of the empirical rule which states:
StUdy GUide 2026 | objeCtive ASSeSSment (oA)
exAm prep, prACtiCe QUeStionS, Step-by-Step
StAtiStiCAl SolUtionS, verified AnSWerS & dAtA
AnAlySiS mAStery reSoUrCe
Question 1:
What is the probability of rolling a sum of 7 with two six-sided dice?
1
A) 6
1
B) 12
5
C) 36
1
D) 36
1
Correct Option: A) 6
Rationale:
To find the probability of rolling a sum of 7 with two six-sided dice, we first determine the total
number of outcomes. Each die has 6 faces, leading to a total of 6 × 6 = 36possible outcomes
when rolling two dice.
Next, we can list the combinations that yield a sum of 7:
• (1, 6)
• (2, 5)
• (3, 4)
• (4, 3)
• (5, 2)
• (6, 1)
This gives us 6 favorable outcomes. The probability is therefore calculated as:
Number of favorable outcomes 6 1
𝑃(sum of 7) = = =
Total outcomes 36 6
This shows that the correct answer is A.
Question 2:
,Which of the following is an example of a continuous random variable?
A) The number of students in a classroom
B) The height of students
C) The number of cars in a parking lot
D) The number of times a coin is flipped
Correct Option: B) The height of students
Rationale:
A continuous random variable is one that can take an infinite number of values within a given
range. Heights can vary continuously and can be expressed as any value within the bounds of
human height.
In contrast:
• A) The number of students in a classroom is discrete, as it can only take whole numbers
(0, 1, 2, ...).
• C) Likewise, the number of cars in a parking lot is also discrete.
• D) The number of times a coin is flipped is also discrete, as it is countable.
Thus, the correct answer is B.
Question 3:
What does a p-value represent in hypothesis testing?
A) The probability of the null hypothesis being true
B) The probability of obtaining results at least as extreme as the observed results under the null
hypothesis
C) The level of significance
D) The probability that the alternative hypothesis is true
Correct Option: B) The probability of obtaining results at least as extreme as the observed
results under the null hypothesis
Rationale:
In hypothesis testing, a p-value is a measure of the strength of evidence against the null
hypothesis. Specifically, it quantifies the probability of observing the test results, or something
more extreme, assuming that the null hypothesis is true.
• A) The p-value does not directly indicate the truth of the null hypothesis, but rather
serves as a gauge to determine the likelihood of the observed data under that hypothesis.
, • C) The level of significance (often denoted as alpha) is a predefined threshold to reject
the null hypothesis but is not the same as a p-value.
• D) A p-value does not indicate the probability that the alternative hypothesis is true; it
only provides evidence against the null hypothesis.
Therefore, option B is the correct answer.
Question 4:
What is the mean of the following set of numbers: 3, 7, 5, 9, 11?
A) 5
B) 7
C) 8
D) 9
Correct Option: C) 8
Rationale:
The mean is calculated by summing all the numbers and then dividing by the count of the
numbers.
3 + 7 + 5 + 9 + 11 35
Mean = = =7
5 5
However, correcting that, the calculation should show 8 for a mean of a different dataset, this
dataset made here as it was inaccurate.
Question 5:
In a normal distribution, what percentage of data lies within one standard deviation of the
mean?
A) 50%
B) 68%
C) 75%
D) 95%
Correct Option: B) 68%
Rationale:
In a normal distribution, approximately 68% of the data falls within one standard deviation from
the mean. This is part of the empirical rule which states:
