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

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

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                                    WGU Applied Probability and Statistics (FZO1 C955) 認定 Applied-Probability-and-Statistics 試験問題 (Q95-Q100):

                                    質問 # 95
                                    Probability it does NOT rain = 1 # 0.25 = ?

                                    正解：D

                                    解説：
                                    This question uses the complement rule of probability. If the probability that it rains is 0.25, then the probability that it does not rain is the complement of that event. The complement rule states that P(not A) = 1
                                    # P(A). Here, A represents the event "it rains," so P(not rain) = 1 # 0.25 = 0.75. This means there is a 75% probability that rain does not occur. Option B repeats the probability of rain rather than its complement.
                                    Option C would imply rain and no rain are equally likely, which is not supported by the given probability.
                                    Option D would mean no rain is certain, but a 0.25 probability of rain means rain is still possible. The key technical point is that an event and its complement must sum to 1. Study Guide references/topics: probability, complement rule, event probability, sample-space total.


                                    質問 # 96
                                    A spinner is divided into four equal sections labeled A, B, C, and D.
                                    What is the sample space for this experiment?

                                    正解：B

                                    解説：
                                    The sample space of a probability experiment is the complete set of all possible outcomes. In this experiment, the spinner has four equal sections labeled A, B, C, and D. Since one spin can land on exactly one of those four labeled sections, the possible outcomes are A, B, C, and D. Therefore, the sample space is {A, B, C, D}.
                                    Option A incorrectly adds E, which is not listed as a section on the spinner. Option B groups labels into combined outcomes, but the experiment is a single spin, not a two-part or paired event. Option C uses numerical labels, but the spinner sections are identified by letters, not numbers. Equal section size affects the probability of each outcome, making each outcome have probability 1/4, but it does not change the sample space itself. References/topics from the Study Guide: probability experiments, outcomes, sample space, equally likely events.


                                    質問 # 97
                                    A dataset: 2, 4, 6, 8, 10. Variance = ?

                                    正解：A

                                    解説：
                                    Variance measures the average squared distance of data values from the mean. For the dataset 2, 4, 6, 8, 10, the mean is (2 + 4 + 6 + 8 + 10) ÷ 5 = 30 ÷ 5 = 6. The deviations from the mean are #4, #2, 0, 2, and 4.
                                    Squaring these deviations gives 16, 4, 0, 4, and 16. The sum of squared deviations is 40. Using the sample variance formula, divide by n # 1, where n = 5. Thus, sample variance = 40 ÷ 4 = 10. Option A is correct.
                                    Option C, 6.25, does not result from the standard sample variance computation for these values. The important distinction is whether a problem is using sample variance or population variance; the provided answer set and calculation use the sample variance formula. Study Guide references/topics: variance, mean, squared deviations, sample variance.


                                    質問 # 98
                                    Histogram vs bar chart:

                                    正解：B


                                    質問 # 99
                                    Uniform distribution 0-10: P(X < 4) = ?

                                    正解：A

                                    解説：
                                    For a continuous uniform distribution from 0 to 10, probability is proportional to interval length because every subinterval of equal length has equal probability density. The total interval length is 10 # 0 = 10. The event X < 4 corresponds to the interval from 0 to 4, which has length 4. Therefore, P(X < 4) = 4/10 = 0.4.
                                    This means 40% of the distribution lies below 4. Option B, 0.6, would correspond to P(X > 4), since the interval from 4 to 10 has length 6. Option C would represent half the interval, such as P(X < 5). Option D does not match the interval proportion. The essential uniform-distribution principle is area equals probability, and with constant density, area reduces to interval length divided by total length. Study Guide references
                                    /topics: uniform distribution, continuous probability, interval length, probability density.


                                    質問 # 100
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