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

SectionObjectives
Topic 1: Probability Distributions- Continuous distributions
  • 1. Normal distribution
    • 2. Standard normal and z-scores
      - Discrete distributions
      • 1. Binomial distribution
        • 2. Poisson distribution (introductory use cases)
          Topic 2: Descriptive Statistics- Data summarization
          • 1. Measures of central tendency (mean, median, mode)
            • 2. Measures of variability (range, variance, standard deviation)
              - Data visualization
              • 1. Histograms and frequency distributions
                • 2. Box plots and interpretation
                  Topic 3: Statistical Inference- Hypothesis testing
                  • 1. t-tests and z-tests (basic application)
                    • 2. Null and alternative hypotheses
                      - Estimation
                      • 1. Confidence intervals for means and proportions
                        Topic 4: Regression and Correlation- Relationship analysis
                        • 1. Simple linear regression basics
                          • 2. Correlation coefficient interpretation
                            Topic 5: Probability- Probability rules
                            • 1. Bayes’ theorem (introductory level)
                              • 2. Addition and multiplication rules
                                - Fundamental probability concepts
                                • 1. Conditional probability and independence
                                  • 2. Events and sample spaces

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                                    WGU Applied Probability and Statistics (FZO1 C955) 認定 Applied-Probability-and-Statistics 試験問題 (Q134-Q139):

                                    質問 # 134
                                    Z-test used when:

                                    正解:D

                                    解説:
                                    A z-test for a population mean is used when the population standard deviation # is known and the sampling distribution of the test statistic can be treated as normal. The test statistic has the form z = (sample statistic # hypothesized parameter) divided by the standard error. Knowing # allows the standard error to be computed using #/#n rather than estimating it with the sample standard deviation. Option B describes the common setting for a t-test, not a z-test. Option C is not sufficient by itself; small samples generally require stronger normality assumptions and often favor t-procedures when # is unknown. Option D is unrelated to the classic z- test for a mean, though z-tests can also be used for proportions under appropriate large-sample conditions. In the provided answer set, the defining condition is that the population standard deviation is known. Study Guide references/topics: z-test, population standard deviation, standard error, hypothesis testing.


                                    質問 # 135
                                    A fitness center owner notices that gym attendance increases as the number of daylight hours increases. The owner calculates a correlation coefficient between daylight hours and gym attendance of r = 0.72.
                                    Based on this information, what can be concluded?

                                    正解:B

                                    解説:
                                    The correlation coefficient r measures the direction and strength of a linear association between two quantitative variables. Since r = 0.72 is positive, the relationship is positive: as daylight hours increase, gym attendance tends to increase. The value 0.72 also indicates a moderately strong to strong linear association because it is closer to 1 than to 0. However, correlation alone does not establish causation. Even though daylight hours and gym attendance move together, other variables could influence attendance, such as weather, seasonal routines, work schedules, or fitness promotions. Therefore, the valid conclusion is that there is a positive association, not a proven causal relationship. Options A and B are incorrect because they describe a negative relationship, which conflicts with the positive correlation coefficient. Option D overstates the evidence by claiming causation. References/topics from the Study Guide: correlation coefficient, positive association, linear relationship, correlation versus causation.


                                    質問 # 136
                                    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:A

                                    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 # 137
                                    Uniform distribution 0-5: P(X < 3) = ?

                                    正解:B

                                    解説:
                                    For a continuous uniform distribution on the interval from 0 to 5, probability is proportional to interval length.
                                    The total interval length is 5 # 0 = 5. The event X < 3 corresponds to the interval from 0 to 3, which has length 3. Therefore, P(X < 3) = 3/5 = 0.6. This works because the uniform distribution assigns constant density across the entire interval, so any subinterval's probability equals its length divided by the total length.
                                    Option B would correspond to half the interval, such as X < 2.5. Option C would correspond to length 2 out of
                                    5. Option D incorrectly treats the cutoff value 3 as if it were a percentage rather than an interval boundary.
                                    The correct answer is 0.6, meaning 60% of the uniform distribution lies below 3. Study Guide references
                                    /topics: uniform distribution, continuous probability, interval length, probability density.


                                    質問 # 138
                                    Standard error decreases when:

                                    正解:D

                                    解説:
                                    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.


                                    質問 # 139
                                    ......

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