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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. Basic probability rules
        • 2. Conditional probability
          • 3. Independent vs dependent events
            Descriptive Statistics- 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)
                  - Two Variable Data Analysis
                  • 1. Correlation
                    • 2. Scatter plots interpretation
                      • 3. Outliers and relationships
                        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
                                Regression and Modeling- Linear Relationships
                                • 1. Simple linear regression
                                  • 2. Slope and intercept interpretation

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                                    WGU Applied Probability and Statistics (FZO1 C955) 認定 Applied-Probability-and-Statistics 試験問題 (Q110-Q115):

                                    質問 # 110
                                    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：C

                                    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 # 111
                                    Regression R² = 0.64. Interpretation?

                                    正解：A

                                    解説：
                                    The coefficient of determination, R², measures the proportion of variability in the response variable Y that is explained by the regression model using explanatory variable X. If R² = 0.64, then 64% of the variation in Y is explained by its linear relationship with X. The remaining 36% is unexplained by the model and may reflect other variables, random variation, measurement error, or nonlinear patterns. Option B is incorrect because R² is not the same as correlation. In simple linear regression, correlation r would be either +0.8 or #0.8, depending on the slope direction, because r² = 0.64. Option C is incorrect because the slope measures change in Y per one-unit change in X, not explained variation. Option D is incorrect because R² is not a probability of making a correct prediction. It is a proportion of variation accounted for by the model. Study Guide references
                                    /topics: regression, coefficient of determination, explained variation, linear modeling.


                                    質問 # 112
                                    Probability of drawing red card from deck = ?

                                    正解：B

                                    解説：
                                    A standard deck has 52 cards divided into four suits: hearts, diamonds, clubs, and spades. Hearts and diamonds are red, while clubs and spades are black. Each suit has 13 cards, so the number of red cards is 13 +
                                    13 = 26. The probability of drawing a red card is therefore the number of favorable outcomes divided by the total number of outcomes: 26/52. This simplifies to 1/2. Option B, 1/4, would describe the probability of drawing one specific suit, such as hearts only. Option C, 1/13, would describe one specific rank in the deck, such as a particular value across suits. Option D does not correspond to the card structure of a standard deck.
                                    Since exactly half the deck is red, the correct probability is 26/52 = 1/2. Study Guide references/topics: card probability, favorable outcomes, sample space, theoretical probability.


                                    質問 # 113
                                    Mean of Poisson # = 5 = ?

                                    正解：B

                                    解説：
                                    For a Poisson distribution, the parameter # represents the mean number of events occurring in a fixed interval.
                                    Therefore, if # = 5, the mean is 5. This means that over many repeated intervals of the same size, the long-run average number of events per interval would be 5. The Poisson distribution is used for count data, such as calls per hour, accidents per week, or defects per batch, when events occur independently and at a constant average rate. A special property of the Poisson distribution is that its variance also equals #, so in this case the variance would also be 5. However, the question asks for the mean, so the direct answer is 5. Options B, C, and D are not supported by the stated parameter. Study Guide references/topics: Poisson distribution, # parameter, expected value, count data.


                                    質問 # 114
                                    A teacher plots the test scores of a class using the box plot.

                                    What is true about the test scores?

                                    正解：D

                                    解説：
                                    A box plot displays the five-number summary of a quantitative data set: minimum, first quartile, median, third quartile, and maximum. The median is represented by the vertical line inside the box. In the given box plot, that internal vertical line is positioned at 80 on the score axis. Therefore, the median test score for Class A is
                                    80 points. The value 70 corresponds to the left edge of the box, which represents the first quartile, not the median. The value near 88 represents the right edge of the box, which is the third quartile. The whiskers extend to the approximate minimum and maximum scores, but those values do not determine the median. The median divides the ordered data into two equal halves, meaning about 50% of the students scored at or below
                                    80 and about 50% scored at or above 80. References/topics from the Study Guide: box plots, five-number summary, median, quartiles.


                                    質問 # 115
                                    ......

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