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

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

                                    >> Applied-Probability-and-Statistics模擬解説集 <<

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                                    WGU Applied Probability and Statistics (FZO1 C955) 認定 Applied-Probability-and-Statistics 試験問題 (Q125-Q130):

                                    質問 # 125
                                    95% confidence interval for mean = (45, 55). Which statement is correct?

                                    正解:C

                                    解説:
                                    A 95% confidence interval provides a plausible range of values for an unknown population mean based on sample data. The interval (45, 55) means the method used to construct the interval captures the true population mean in approximately 95% of repeated samples under the same conditions. In practical exam language, the correct interpretation is that the population mean is estimated to lie within the interval with 95% confidence. Option B states the midpoint of the interval, 50, but the question asks for the correct confidence interval interpretation, not just the center. Option C is incorrect because the population mean is not always the upper endpoint. Option D is imprecise because once an interval is computed, it is fixed; the confidence level refers to the long-run success rate of the procedure, not a changing probability attached to that exact fixed interval. Study Guide references/topics: confidence intervals, population mean, point estimate, margin of error.


                                    質問 # 126
                                    Type II error # is:

                                    正解:C

                                    解説:
                                    A Type II error occurs when the null hypothesis is false but the test fails to reject it. Many introductory answer choices phrase this as "accept H# when false," though the more technically careful wording is "fail to reject H# when false." This is a false negative: the real effect or difference exists, but the test does not detect sufficient evidence. The probability of a Type II error is denoted #. Option B describes a Type I error, which is rejecting a true null hypothesis. Option C is incorrect because 1 # # is not #; # is the Type I error probability, while 1 # # is statistical power. Option D is too vague and does not identify a formal hypothesis- testing error. The defining condition for Type II error is missing a real effect by failing to reject a false null hypothesis. Study Guide references/topics: Type II error, beta, hypothesis testing, statistical power.


                                    質問 # 127
                                    Determine x:
                                    4 + x = 6 # x

                                    正解:A

                                    解説:
                                    The equation 4 + x = 6 # x is a linear equation in one variable. To solve it, collect variable terms on one side and constant terms on the other. Add x to both sides to eliminate the negative x on the right: 4 + 2x = 6. Then subtract 4 from both sides: 2x = 2. Finally, divide both sides by 2, giving x = 1. This value can be verified directly in the original equation. Substituting x = 1 gives 4 + 1 = 5 on the left and 6 # 1 = 5 on the right, so both sides are equal. Option A gives 4 = 6, which is false. Option C gives 6 = 4, also false. Option D gives 9 =
                                    1, which is not valid. The correct solution is the value that balances both sides of the equation. References
                                    /topics from the Study Guide: basic algebra, solving linear equations, inverse operations, substitution checks.


                                    質問 # 128
                                    There are 12 cell phone charging cords available at a store for purchase. The length of each charging cord in inches is reflected as 3, 3, 4, 6, 6, 6, 6, 7, 10, 10, 11, and 12, respectively.
                                    What are the mean of these data?

                                    正解:A

                                    解説:
                                    The mean is the arithmetic average of a data set. To find it, add all values and divide by the number of values.
                                    The cord lengths are 3, 3, 4, 6, 6, 6, 6, 7, 10, 10, 11, and 12. Their sum is 84. Since there are 12 charging cords, divide 84 by 12 to obtain 7. Therefore, the mean cord length is 7 inches. This value represents the balance point of the distribution, not necessarily a value that must occur most often. In this data set, 6 appears most frequently, so 6 is the mode, but the question asks for the mean. Option B, 8, and option C, 9, are too large because several values are below 7. Option D, 6, identifies the most common value rather than the average. References/topics from the Study Guide: mean, measures of center, quantitative data, arithmetic average.


                                    質問 # 129
                                    A person has a .5 probability of taking a train to work, a .3 probability of carpooling, and a .2 probability of walking. The probability of being late is .2 when taking the train, .1 when carpooling, and .05 when walking.
                                    What is the probability of taking the train and being on time, or walking and being on time?

                                    正解:D

                                    解説:
                                    This problem combines complements, joint probabilities, and addition of mutually exclusive outcomes. First compute the probability of taking the train and being on time. The probability of being late when taking the train is .2, so the probability of being on time by train is 1 # .2 = .8. Thus, P(train and on time) = .5 × .8 = .40.
                                    Next compute the probability of walking and being on time. The probability of being late when walking is .
                                    05, so the probability of being on time while walking is 1 # .05 = .95. Thus, P(walking and on time) = .2 × .95
                                    = .19. Since a person cannot both take the train and walk as the selected commuting mode, these outcomes are mutually exclusive. Add the two results: .40 + .19 = .59. References/topics from the Study Guide:
                                    complements, conditional probability, joint probability, addition rule.


                                    質問 # 130
                                    ......

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