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

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

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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
                                    Random variable X = number of heads in 4 coin flips #

                                    正解：A

                                    解説：
                                    The random variable X counts the number of heads obtained in 4 coin flips. Since it is a count, it can take only specific whole-number values: 0, 1, 2, 3, or 4. It cannot take fractional values such as 2.5 heads. A random variable with countable possible outcomes is classified as discrete. This situation also fits a binomial framework because there is a fixed number of independent trials, each trial has two outcomes, and the probability of heads remains constant for a fair coin. A continuous random variable, by contrast, can take any value over an interval, such as time, weight, or height. The number of heads is not measured on a continuum; it is counted. Therefore, the correct classification is discrete. Study Guide references/topics: discrete random variables, binomial setting, coin-flip outcomes, probability distributions.


                                    質問 # 96
                                    The dot plot illustrates the frequency of outdoor games played by students per week.

                                    Which statement is true?

                                    正解：C

                                    解説：
                                    The dot plot shows a distribution centered near 3 days, with substantial frequencies at 2, 3, and 4 days and smaller frequencies at the extremes of 1 and 5 days. This shape is reasonably balanced around the center.
                                    When a distribution is approximately symmetric, the mean and median tend to be close because the lower and higher values balance each other. The median identifies the middle observation after the data are ordered, and the mean represents the balance point of the distribution. Since the tallest stack is near 3 days and the surrounding stacks on 2 and 4 days are comparable, the center of the data is approximately 3 days by both measures. There is no strong skew to pull the mean far above or below the median. Therefore, the best statement is that the mean is almost the same as the median. Options B and C would require clear skew or extreme imbalance, which the dot plot does not show. References/topics from the Study Guide: dot plots, mean, median, distribution shape, symmetry.


                                    質問 # 97
                                    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：C

                                    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 # 98
                                    What is the mode of this dataset: 3, 5, 7, 7, 10?

                                    正解：C

                                    解説：
                                    The mode is the value that occurs most frequently in a data set. In the set 3, 5, 7, 7, 10, the value 3 appears once, 5 appears once, 10 appears once, and 7 appears twice. Since 7 has the highest frequency, it is the mode.
                                    This question tests recognition of a measure of center that differs from the mean and median. The mean would require summing all values and dividing by the number of observations, while the median would identify the middle value after ordering the data. The data are already ordered, and the middle value is also 7, but the reason the correct answer is 7 here is specifically because it appears more often than any other value. Options A, B, and D each name values that occur only once, so none can be the mode. A dataset may have one mode, multiple modes, or no mode, but this dataset is unimodal. References/topics from the Study Guide: descriptive statistics, measures of center, frequency, mode.


                                    質問 # 99
                                    A city council surveys residents and business owners about a proposed new public transportation system. The results of the survey are shown in the following 2 × 2 contingency table.

                                    Which statement is true?

                                    正解：C

                                    解説：
                                    This question requires comparing conditional percentages from a two-way table. For residents, 150 out of 200 are in favor of the proposed transportation system. The resident support rate is therefore 150/200 = 0.75, or
                                    75%. For business owners, 30 out of 100 are in favor. The business owner support rate is 30/100 = 0.30, or
                                    30%. The difference is 75% # 30% = 45 percentage points, which is a large gap. Therefore, a resident is much more likely than a business owner to favor the new transportation system. Option A understates the magnitude of the difference by calling it slight. Options B and C reverse the direction of the comparison because residents have the higher support rate, not the lower one. The appropriate statistical tool here is conditional percentage because support is being compared within each respondent group. References/topics from the Study Guide: contingency tables, conditional percentages, two-variable categorical data, comparative proportions.


                                    質問 # 100
                                    ......

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