WGU C955 Applied Probability and Statistics Final Exam
Actual 2026 / with Verified Answers Grade A+ Guarantee - 124
Questions
Comprehensive examination on WGU C955 Applied Probability and Statistics Final Exam Actual 2026 / with
Verified Answers Grade A+ Guarantee. It contains 124 multiple-choice questions, each with four distractors and a
fully worked rationale that explains why the keyed answer is correct. Content is organized into 7 focused sections:
Descriptive Statistics, Probability, Discrete Probability Distributions, Continuous Probability Distributions,
Sampling Distributions and Estimation, Hypothesis Testing, Correlation and Regression. Targeted learning
outcomes include: Demonstrate mastery of core concepts. Every item has been reviewed for clinical accuracy,
current guidelines, and clarity so that students can study with confidence and self-correct as they work through
the bank. Use it as a high-yield review immediately before the exam, or as a structured practice tool during the
unit - the rationales double as concise teaching notes. The recommended writing time is 3 hours, with a passing
score of 70%. Aligned with Aligned with US university standards. standards and reflects the question style
commonly seen on accredited program examinations. Students consistently achieving above the cut score on this
bank have historically gone on to earn A+ on the corresponding course exam. Read every stem carefully -
distractors are written to look plausible, and the best answer is sometimes the one that addresses the patient's
most immediate physiological or safety need. Where multiple options appear correct, prioritize airway, breathing,
circulation, safety, and Maslow's hierarchy before psychosocial interventions. Treat each rationale as a
Section 1: Descriptive Statistics (Questions 1-9)
1 A data set contains the annual incomes (in thousands) of 100 employees at a
firm. The mean income is $65,000 and the median is $62,000. If the highest
income (originally $250,000) is replaced by $500,000, what happens to the
mean and median?
A) Both the mean and median increase.
B) The mean increases, but the median remains unchanged.
C) The mean remains unchanged, but the median increases.
D) The mean increases, and the median might increase slightly.
Answer: B
Rationale: The mean is sensitive to extreme values, so replacing a high value
with an even higher value will increase the mean. The median is resistant to
outliers, and since the rank order does not change (the highest value remains
the highest), the median remains unchanged.
2 Two investment portfolios have the same mean annual return of 8%.
Portfolio A has a standard deviation of 12%, while Portfolio B has a standard
deviation of 5%. Which portfolio is riskier based on the coefficient of
variation?
A) Portfolio A, because it has a higher CV.
,B) Portfolio B, because it has a lower CV.
C) Both have the same risk because the mean returns are equal.
D) Cannot be determined without the covariance.
Answer: A
Rationale: The coefficient of variation (CV) is the ratio of standard deviation to
mean, expressed as a percentage. For Portfolio A, CV = 12%/8% = 1.5; for
Portfolio B, CV = 5%/8% = 0.625. A higher CV indicates more risk per unit of
return, so Portfolio A is riskier.
3 Given a dataset: {4, 8, 15, 16, 23, 42}. What is the interquartile range (IQR)?
A) 12
B) 14
C) 16
D) 18
Answer: C
Rationale: Sorted data: 4,8,15,16,24,42. Median = (15+16)/2 = 15.5. Q1 =
median of lower half (4,8,15) = 8. Q3 = median of upper half (16,24,42) = 24.
IQR = Q3 - Q1 = 24 - 8 = 16.
4 A box plot shows the following five-number summary for a dataset:
Minimum = 10, Q1 = 20, Median = 25, Q3 = 40, Maximum = 100. Which of
the following best describes the shape of the distribution?
A) Symmetric
B) Left-skewed
C) Right-skewed
D) Uniform
Answer: C
Rationale: The right whisker (from Q3=40 to Max=100) is much longer than
the left whisker (from Min=10 to Q1=20), and the median (25) is closer to Q1
than to Q3, indicating a long tail to the right. Thus, the distribution is
right-skewed.
5 A dataset has a mean of 50 and a standard deviation of 10. Using
Chebyshev's theorem, what is the minimum percentage of data that lies
between 30 and 70?
A) 68%
,B) 75%
C) 89%
D) 95%
Answer: B
Rationale: The interval (30,70) is 20 units from the mean, which corresponds to
k=2 standard deviations (since 10*2=20). Chebyshev's theorem states that at
least 1 - 1/k² = 1 - 1/4 = 0.75 or 75% of the data lies within k=2 standard
deviations of the mean.
6 In a dataset, the mean is 45 and the standard deviation is 8. A data point has
a z-score of -1.5. What is the value of this data point?
A) 33
B) 45
C) 57
D) 57
Answer: A
Rationale: The z-score formula is z = (x - ¼)/Ã. Rearranging: x = ¼ + zà = 45 +
(-1.5)*8 = 45 - 12 = 33.
7 Which measure of central tendency is most appropriate for a dataset that is
bimodal and contains outliers?
A) Mean
B) Median
C) Mode
D) Midrange
Answer: C
Rationale: For a bimodal distribution, the mean and median may not represent
typical values. The mode directly identifies the most frequent values, so it is
most appropriate. Outliers affect the mean and midrange, but the median is not
ideal for bimodal data either as it may lie in a sparse region.
8 A histogram of exam scores shows a bar from 60-70 with a frequency of 5,
70-80 with frequency 12, 80-90 with frequency 8, and 90-100 with
frequency 3. What is the approximate mean score?
A) 75
B) 77
, C) 78
D) 80
Answer: C
Rationale: Use midpoint of each interval: 65, 75, 85, 95. Multiply by
frequencies: 65*5=325, 75*12=900, 85*8=680, 95*3=285. Sum =
325+900+680+285=2190. Total frequency = 5+12+8+3=28. Mean 2190/28
78.21, so approximately 78.
9 Which of the following statements about the standard deviation is false?
A) It is measured in the same units as the data.
B) It is always nonnegative.
C) It is resistant to outliers.
D) It can be zero if all data values are equal.
Answer: C
Rationale: Standard deviation is not resistant to outliers; it is sensitive because
it uses squared deviations from the mean. A single outlier can inflate the
standard deviation. Options A, B, and D are true: standard deviation has the
same units as data, is nonnegative, and is zero when all values are identical.
Section 2: Probability (Questions 10-38)
10 A diagnostic test for a disease has a sensitivity of 95% and a specificity of
90%. The prevalence of the disease in the population is 2%. If a randomly
selected individual tests positive, what is the probability that they actually
have the disease?
A) 0.162
B) 0.190
C) 0.022
D) 0.857
Answer: A
Rationale: Use Bayes' theorem: P(Disease|Positive) = (0.95*0.02) / (0.95*0.02
+ 0.10*0.98) 0.162. Option B incorrectly uses specificity as 1-sensitivity; C is
the prevalence; D is sensitivity given positive.
Actual 2026 / with Verified Answers Grade A+ Guarantee - 124
Questions
Comprehensive examination on WGU C955 Applied Probability and Statistics Final Exam Actual 2026 / with
Verified Answers Grade A+ Guarantee. It contains 124 multiple-choice questions, each with four distractors and a
fully worked rationale that explains why the keyed answer is correct. Content is organized into 7 focused sections:
Descriptive Statistics, Probability, Discrete Probability Distributions, Continuous Probability Distributions,
Sampling Distributions and Estimation, Hypothesis Testing, Correlation and Regression. Targeted learning
outcomes include: Demonstrate mastery of core concepts. Every item has been reviewed for clinical accuracy,
current guidelines, and clarity so that students can study with confidence and self-correct as they work through
the bank. Use it as a high-yield review immediately before the exam, or as a structured practice tool during the
unit - the rationales double as concise teaching notes. The recommended writing time is 3 hours, with a passing
score of 70%. Aligned with Aligned with US university standards. standards and reflects the question style
commonly seen on accredited program examinations. Students consistently achieving above the cut score on this
bank have historically gone on to earn A+ on the corresponding course exam. Read every stem carefully -
distractors are written to look plausible, and the best answer is sometimes the one that addresses the patient's
most immediate physiological or safety need. Where multiple options appear correct, prioritize airway, breathing,
circulation, safety, and Maslow's hierarchy before psychosocial interventions. Treat each rationale as a
Section 1: Descriptive Statistics (Questions 1-9)
1 A data set contains the annual incomes (in thousands) of 100 employees at a
firm. The mean income is $65,000 and the median is $62,000. If the highest
income (originally $250,000) is replaced by $500,000, what happens to the
mean and median?
A) Both the mean and median increase.
B) The mean increases, but the median remains unchanged.
C) The mean remains unchanged, but the median increases.
D) The mean increases, and the median might increase slightly.
Answer: B
Rationale: The mean is sensitive to extreme values, so replacing a high value
with an even higher value will increase the mean. The median is resistant to
outliers, and since the rank order does not change (the highest value remains
the highest), the median remains unchanged.
2 Two investment portfolios have the same mean annual return of 8%.
Portfolio A has a standard deviation of 12%, while Portfolio B has a standard
deviation of 5%. Which portfolio is riskier based on the coefficient of
variation?
A) Portfolio A, because it has a higher CV.
,B) Portfolio B, because it has a lower CV.
C) Both have the same risk because the mean returns are equal.
D) Cannot be determined without the covariance.
Answer: A
Rationale: The coefficient of variation (CV) is the ratio of standard deviation to
mean, expressed as a percentage. For Portfolio A, CV = 12%/8% = 1.5; for
Portfolio B, CV = 5%/8% = 0.625. A higher CV indicates more risk per unit of
return, so Portfolio A is riskier.
3 Given a dataset: {4, 8, 15, 16, 23, 42}. What is the interquartile range (IQR)?
A) 12
B) 14
C) 16
D) 18
Answer: C
Rationale: Sorted data: 4,8,15,16,24,42. Median = (15+16)/2 = 15.5. Q1 =
median of lower half (4,8,15) = 8. Q3 = median of upper half (16,24,42) = 24.
IQR = Q3 - Q1 = 24 - 8 = 16.
4 A box plot shows the following five-number summary for a dataset:
Minimum = 10, Q1 = 20, Median = 25, Q3 = 40, Maximum = 100. Which of
the following best describes the shape of the distribution?
A) Symmetric
B) Left-skewed
C) Right-skewed
D) Uniform
Answer: C
Rationale: The right whisker (from Q3=40 to Max=100) is much longer than
the left whisker (from Min=10 to Q1=20), and the median (25) is closer to Q1
than to Q3, indicating a long tail to the right. Thus, the distribution is
right-skewed.
5 A dataset has a mean of 50 and a standard deviation of 10. Using
Chebyshev's theorem, what is the minimum percentage of data that lies
between 30 and 70?
A) 68%
,B) 75%
C) 89%
D) 95%
Answer: B
Rationale: The interval (30,70) is 20 units from the mean, which corresponds to
k=2 standard deviations (since 10*2=20). Chebyshev's theorem states that at
least 1 - 1/k² = 1 - 1/4 = 0.75 or 75% of the data lies within k=2 standard
deviations of the mean.
6 In a dataset, the mean is 45 and the standard deviation is 8. A data point has
a z-score of -1.5. What is the value of this data point?
A) 33
B) 45
C) 57
D) 57
Answer: A
Rationale: The z-score formula is z = (x - ¼)/Ã. Rearranging: x = ¼ + zà = 45 +
(-1.5)*8 = 45 - 12 = 33.
7 Which measure of central tendency is most appropriate for a dataset that is
bimodal and contains outliers?
A) Mean
B) Median
C) Mode
D) Midrange
Answer: C
Rationale: For a bimodal distribution, the mean and median may not represent
typical values. The mode directly identifies the most frequent values, so it is
most appropriate. Outliers affect the mean and midrange, but the median is not
ideal for bimodal data either as it may lie in a sparse region.
8 A histogram of exam scores shows a bar from 60-70 with a frequency of 5,
70-80 with frequency 12, 80-90 with frequency 8, and 90-100 with
frequency 3. What is the approximate mean score?
A) 75
B) 77
, C) 78
D) 80
Answer: C
Rationale: Use midpoint of each interval: 65, 75, 85, 95. Multiply by
frequencies: 65*5=325, 75*12=900, 85*8=680, 95*3=285. Sum =
325+900+680+285=2190. Total frequency = 5+12+8+3=28. Mean 2190/28
78.21, so approximately 78.
9 Which of the following statements about the standard deviation is false?
A) It is measured in the same units as the data.
B) It is always nonnegative.
C) It is resistant to outliers.
D) It can be zero if all data values are equal.
Answer: C
Rationale: Standard deviation is not resistant to outliers; it is sensitive because
it uses squared deviations from the mean. A single outlier can inflate the
standard deviation. Options A, B, and D are true: standard deviation has the
same units as data, is nonnegative, and is zero when all values are identical.
Section 2: Probability (Questions 10-38)
10 A diagnostic test for a disease has a sensitivity of 95% and a specificity of
90%. The prevalence of the disease in the population is 2%. If a randomly
selected individual tests positive, what is the probability that they actually
have the disease?
A) 0.162
B) 0.190
C) 0.022
D) 0.857
Answer: A
Rationale: Use Bayes' theorem: P(Disease|Positive) = (0.95*0.02) / (0.95*0.02
+ 0.10*0.98) 0.162. Option B incorrectly uses specificity as 1-sensitivity; C is
the prevalence; D is sensitivity given positive.
