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

SectionObjectives
Topic 1: Descriptive Statistics- Two Variable Data Analysis
  • 1. Outliers and relationships
    • 2. Scatter plots interpretation
      • 3. Correlation
        - Single Variable Data Analysis
        • 1. Data visualization (histograms, box plots)
          • 2. Measures of dispersion (variance, standard deviation, range)
            • 3. Measures of central tendency (mean, median, mode)
              Topic 2: Regression and Modeling- Linear Relationships
              • 1. Slope and intercept interpretation
                • 2. Simple linear regression
                  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- Fundamental Probability Concepts
                          • 1. Conditional probability
                            • 2. Basic probability rules
                              • 3. Independent vs dependent events
                                - Probability Distributions
                                • 1. Binomial distribution basics
                                  • 2. Normal distribution

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                                    WGU Applied Probability and Statistics (FZO1 C955) 認定 Applied-Probability-and-Statistics 試験問題 (Q157-Q162):

                                    質問 # 157
                                    Boxplot shows:

                                    正解：B

                                    解説：
                                    A boxplot displays the distribution of a quantitative variable using the five-number summary and potential outliers. The main features are the median, first quartile, third quartile, lower whisker, upper whisker, and any marked outliers. The box extends from Q1 to Q3 and represents the interquartile range, which contains the middle 50% of the data. The line inside the box marks the median. Whiskers show the spread of non-outlier values, depending on the graphing convention. Option B is incorrect because a boxplot does not show only the mean; many boxplots do not display the mean at all. Option C is incorrect because variance is a numerical measure of spread, not a standard direct feature of a boxplot. Option D is incorrect because a boxplot is not a probability model. It is a descriptive display for summarizing center, spread, and unusual observations. Study Guide references/topics: boxplots, median, quartiles, interquartile range, outliers.


                                    質問 # 158
                                    A single ball is drawn from an opaque bag that contains red, blue, and green balls. The probability of drawing a red ball is .3, and the probability of drawing a blue ball is .6.
                                    What is the probability of drawing a green ball?

                                    正解：D

                                    解説：
                                    The probabilities of all possible outcomes in a sample space must sum to 1. In this experiment, the bag contains only red, blue, and green balls, so these three outcomes exhaust the sample space. The probability of drawing a red ball is 0.3, and the probability of drawing a blue ball is 0.6. Their combined probability is 0.3 +
                                    0.6 = 0.9. The remaining probability must belong to drawing a green ball. Therefore, P(green) = 1 # 0.9 = 0.1.
                                    This can also be viewed as a complement problem: green is the complement of drawing either red or blue when those are the only other colors available. Option B repeats the red probability, option C would make the total probability exceed 1, and option D is the combined probability of red or blue rather than green.
                                    References/topics from the Study Guide: probability sum rule, complements, sample space, mutually exclusive outcomes.


                                    質問 # 159
                                    Empirical probability = ?

                                    正解：C

                                    解説：
                                    Empirical probability is probability determined from observed data rather than from a purely theoretical model. It is calculated by dividing the number of times an event actually occurs by the total number of trials or observations. For example, if a basketball player makes 72 free throws in 100 attempts, the empirical probability of a made free throw is 72/100 = 0.72. This differs from theoretical probability, which is derived from known equally likely outcomes, such as rolling a 3 on a fair six-sided die. It also differs from a guess or subjective estimate because empirical probability requires actual recorded evidence. The term "uniform" describes a distribution in which outcomes or intervals have equal probability, not the basis for empirical probability. Since the question asks for the definition of empirical probability, the correct selection is observed data. Study Guide references/topics: empirical probability, relative frequency, observed outcomes, probability interpretation.


                                    質問 # 160
                                    Variance formula = ?

                                    正解：B

                                    解説：
                                    The sample variance formula is s² = #(x# # x#)² / (n # 1). In this formula, x# represents each data value, x# is the sample mean, and n is the sample size. The expression x# # x# gives each value's deviation from the mean. Squaring the deviations prevents negative and positive deviations from canceling and emphasizes larger departures. Dividing by n # 1 gives the sample variance, using degrees of freedom to correct bias when estimating population variance from a sample. Option B is the formula for the sample mean, not variance.
                                    Option C squares the mean and does not measure spread. Option D resembles part of the standard deviation process but omits division by n # 1 and is not the variance formula. Variance is foundational because standard deviation is the square root of variance. Study Guide references/topics: variance, sample variance formula, mean deviations, measures of spread.


                                    質問 # 161
                                    In hypothesis testing, rejecting H# when true = ?

                                    正解：B

                                    解説：
                                    A Type I error occurs when the null hypothesis, H#, is true but the test decision rejects it. In plain statistical language, this is a false positive: the analysis concludes that there is evidence of an effect, difference, or relationship when in reality the null condition is true. The probability of making a Type I error is denoted by
                                    #, the significance level, commonly set at 0.05. A Type II error is different; it occurs when the null hypothesis is false but the test fails to reject it. That is a false negative. Option C is incorrect because rejecting a true null is not a correct decision. Option D describes not rejecting or accepting the null, not the stated event. The critical phrase is "rejecting H# when true," which directly defines a Type I error. Study Guide references
                                    /topics: hypothesis testing, null hypothesis, Type I error, significance level.


                                    質問 # 162
                                    ......

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