WGU Applied-Probability-and-Statistics Questions For Guaranteed Success [2026]

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WGU Applied-Probability-and-Statistics Exam Syllabus Topics:

SectionObjectives
Topic 1: Regression and Modeling- Linear Relationships
  • 1. Simple linear regression
    • 2. Slope and intercept interpretation
      Topic 2: Descriptive Statistics- Two Variable Data Analysis
      • 1. Correlation
        • 2. Scatter plots interpretation
          • 3. Outliers and relationships
            - Single Variable Data Analysis
            • 1. Measures of central tendency (mean, median, mode)
              • 2. Measures of dispersion (variance, standard deviation, range)
                • 3. Data visualization (histograms, box plots)
                  Topic 3: Statistical Inference- Hypothesis Testing (Introductory Level)
                  • 1. p-values interpretation
                    • 2. Null vs alternative hypothesis
                      - Estimation and Confidence Intervals
                      • 1. Confidence interval interpretation
                        • 2. Point estimates
                          Topic 4: Probability Theory- Probability Distributions
                          • 1. Binomial distribution basics
                            • 2. Normal distribution
                              - Fundamental Probability Concepts
                              • 1. Basic probability rules
                                • 2. Conditional probability
                                  • 3. Independent vs dependent events

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q145-Q150):

                                    NEW QUESTION # 145
                                    A standard deck of 52 playing cards, 13 with hearts, 13 with diamonds, 13 with clovers, and 13 with spades, is shuffled, and one card is drawn at random.
                                    What is the probability of drawing a heart?

                                    Answer: D

                                    Explanation:
                                    The probability of a simple event is calculated by dividing the number of favorable outcomes by the total number of equally likely outcomes. A standard deck contains 52 cards. The favorable outcomes are the hearts, and the question states that there are 13 hearts in the deck. Therefore, the probability of drawing a heart is 13
                                    /52. This fraction simplifies by dividing both numerator and denominator by 13, giving 1/4. Option A, 1/13, would incorrectly treat one card as favorable out of 13 rather than 13 favorable hearts out of 52 total cards.
                                    Option B, 1/2, would imply that half the deck consists of hearts, which is false. Option D, 1/3, does not correspond to the four equally sized suits in a standard deck. Since the four suits are equally represented, each suit has probability one out of four. References/topics from the Study Guide: theoretical probability, equally likely outcomes, fractions, sample spaces.


                                    NEW QUESTION # 146
                                    Mean of Poisson # = 5 = ?

                                    Answer: D

                                    Explanation:
                                    For a Poisson distribution, the parameter # represents the mean number of events occurring in a fixed interval.
                                    Therefore, if # = 5, the mean is 5. This means that over many repeated intervals of the same size, the long-run average number of events per interval would be 5. The Poisson distribution is used for count data, such as calls per hour, accidents per week, or defects per batch, when events occur independently and at a constant average rate. A special property of the Poisson distribution is that its variance also equals #, so in this case the variance would also be 5. However, the question asks for the mean, so the direct answer is 5. Options B, C, and D are not supported by the stated parameter. Study Guide references/topics: Poisson distribution, # parameter, expected value, count data.


                                    NEW QUESTION # 147
                                    Standard error decreases when:

                                    Answer: B

                                    Explanation:
                                    The standard error of the sample mean is calculated as SE = s/#n, where s is the sample standard deviation and n is the sample size. Since n appears in the denominator, increasing the sample size reduces the standard error, assuming the standard deviation stays constant. This reflects the fact that larger samples produce more stable estimates of the population mean. Option B is incorrect because decreasing sample size increases standard error. Option C is incorrect because a larger standard deviation increases standard error by increasing the numerator. Option D is incorrect because the mean affects the center of the distribution but does not directly determine the standard error. Standard error is about precision: smaller standard error means less sampling variability and a more precise estimate. That is why larger samples are preferred in inference. Study Guide references/topics: standard error, sample size, standard deviation, sampling variability.


                                    NEW QUESTION # 148
                                    The average commute time for workers in a city in 2021 was 35 minutes, with a standard deviation of 5 minutes.
                                    Assuming a normal distribution, which two values encompass 95% of the data?

                                    Answer: C

                                    Explanation:
                                    For a normally distributed variable, the empirical rule states that approximately 95% of observations fall within two standard deviations of the mean. The mean commute time is 35 minutes, and the standard deviation is 5 minutes. Two standard deviations equal 2 × 5 = 10 minutes. Therefore, the interval covering approximately 95% of the data is 35 # 10 to 35 + 10, which gives 25 minutes to 45 minutes. Option B, 30 to
                                    40 minutes, represents only one standard deviation from the mean and would cover approximately 68% of the data, not 95%. Option A extends three standard deviations from the mean and would correspond to roughly
                                    99.7% under the empirical rule. Option D is not centered properly around the mean and does not represent a standard normal interval. The correct interval is symmetric about the mean and uses the standard deviation as the spread measure. References/topics from the Study Guide: normal distribution, empirical rule, mean, standard deviation.


                                    NEW QUESTION # 149
                                    P(A) = 0.3, P(B) = 0.4, A and B independent. P(A and B) = ?

                                    Answer: A

                                    Explanation:
                                    For independent events, the occurrence of one event does not change the probability of the other event. The multiplication rule states that if A and B are independent, then P(A and B) = P(A) × P(B). Here, P(A) = 0.3 and P(B) = 0.4. Therefore, P(A and B) = 0.3 × 0.4 = 0.12. This means there is a 12% probability that both events occur. Option B, 0.7, incorrectly adds the probabilities and would only be part of an "or" calculation, not an "and" calculation. Option D repeats P(A), and option C does not follow from the multiplication rule.
                                    The phrase "A and B independent" is the decisive condition because it permits direct multiplication without adjusting for conditional probability. Study Guide references/topics: independent events, multiplication rule, compound probability, joint probability.


                                    NEW QUESTION # 150
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