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

SectionObjectives
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
        Probability- Fundamental probability concepts
        • 1. Conditional probability and independence
          • 2. Events and sample spaces
            - Probability rules
            • 1. Addition and multiplication rules
              • 2. Bayes’ theorem (introductory level)
                Regression and Correlation- Relationship analysis
                • 1. Correlation coefficient interpretation
                  • 2. Simple linear regression basics
                    Probability Distributions- Continuous distributions
                    • 1. Normal distribution
                      • 2. Standard normal and z-scores
                        - Discrete distributions
                        • 1. Poisson distribution (introductory use cases)
                          • 2. Binomial distribution
                            Descriptive Statistics- Data summarization
                            • 1. Measures of central tendency (mean, median, mode)
                              • 2. Measures of variability (range, variance, standard deviation)
                                - Data visualization
                                • 1. Box plots and interpretation
                                  • 2. Histograms and frequency distributions

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                                    WGU Applied-Probability-and-Statistics Latest Exam Vce - Applied-Probability-and-Statistics Lab Questions

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q72-Q77):

                                    NEW QUESTION # 72
                                    Empirical probability = ?

                                    Answer: B

                                    Explanation:
                                    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.


                                    NEW QUESTION # 73
                                    Review the following inequality:
                                    y < x # 1/2
                                    Which shaded portion in the graphs corresponds to this inequality?



                                    Answer: D

                                    Explanation:
                                    The inequality y < x # 1/2 has boundary line y = x # 1/2. This line has slope 1 and y-intercept #1/2, so it crosses the y-axis slightly below the origin and rises one unit for every one unit moved to the right. Because the inequality is strict, using " < " rather than "#," the boundary line must be dashed, showing that points on the line are not included in the solution set. The solution region must be shaded below the line because y is less than the expression x # 1/2. A useful verification method is the test point (0, 0). Substituting gives 0 < 0 #
                                    1/2, or 0 < #1/2, which is false. Therefore, the region containing the origin should not be shaded. The fourth graph has the dashed boundary with intercept #1/2 and shades the region below the line while excluding the origin. References/topics from the Study Guide: graphing linear inequalities, slope-intercept form, dashed boundaries, test-point method.


                                    NEW QUESTION # 74
                                    A sociologist is investigating the relationship between educational level, high school, bachelor's, master's, and doctorate, and annual income.
                                    How should this study be classified?

                                    Answer: A

                                    Explanation:
                                    This study contains two variables: educational level and annual income. Educational level is categorical because it places individuals into named groups, such as high school, bachelor's, master's, and doctorate.
                                    Although these categories have a natural order, they are still categories rather than measured numerical quantities. Annual income is quantitative because it is measured numerically and can be analyzed using arithmetic summaries such as mean, median, range, and standard deviation. Therefore, the study is classified as categorical-to-quantitative. This classification is important because it determines appropriate statistical displays and summaries. For example, side-by-side box plots or group means could be used to compare annual income across education levels. A categorical-to-categorical study would involve two label-based variables, such as education level and employment sector. A quantitative-to-quantitative study would involve two numerical variables, such as income and years of experience. References/topics from the Study Guide:
                                    categorical variables, quantitative variables, two-variable data classification, comparative summaries.


                                    NEW QUESTION # 75
                                    A teacher plots the test scores of a class using the box plot.

                                    What is true about the test scores?

                                    Answer: B

                                    Explanation:
                                    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.


                                    NEW QUESTION # 76
                                    In a game, a coin is tossed, and a spinner with 8 equal spaces numbered 1 through 8 is spun.
                                    What is the probability of getting heads on the coin and a number less than 3 on the spinner?

                                    Answer: D

                                    Explanation:
                                    This experiment has two independent stages: tossing a coin and spinning a numbered spinner. The probability of getting heads on a fair coin is 1/2. The spinner has 8 equally likely outcomes numbered 1 through 8. A number less than 3 means either 1 or 2, so there are 2 favorable spinner outcomes out of 8 total outcomes.
                                    Thus, P(number less than 3) = 2/8 = 1/4. Since the coin result does not affect the spinner result, the events are independent. For independent events connected by "and," multiply the probabilities: 1/2 × 1/4 = 1/8.
                                    Equivalently, the combined sample space has 2 coin outcomes times 8 spinner outcomes, or 16 total equally likely outcomes. The favorable outcomes are heads with 1 and heads with 2, giving 2/16 = 1/8. References
                                    /topics from the Study Guide: independent events, sample spaces, multiplication rule, theoretical probability.


                                    NEW QUESTION # 77
                                    ......

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