Free PDF Quiz 2026 Perfect Applied-Probability-and-Statistics: Applied Probability and Statistics (FZO1 C955) Training Solutions

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

SectionObjectives
Topic 1: Statistical Inference- Estimation and Confidence Intervals
  • 1. Point estimates
    • 2. Confidence interval interpretation
      - Hypothesis Testing (Introductory Level)
      • 1. p-values interpretation
        • 2. Null vs alternative hypothesis
          Topic 2: 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
                    Topic 3: Regression and Modeling- Linear Relationships
                    • 1. Slope and intercept interpretation
                      • 2. Simple linear regression
                        Topic 4: Descriptive Statistics- Single Variable Data Analysis
                        • 1. Measures of dispersion (variance, standard deviation, range)
                          • 2. Data visualization (histograms, box plots)
                            • 3. Measures of central tendency (mean, median, mode)
                              - Two Variable Data Analysis
                              • 1. Outliers and relationships
                                • 2. Scatter plots interpretation
                                  • 3. Correlation

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q76-Q81):

                                    NEW QUESTION # 76
                                    A marketing analyst is studying the relationship between customer age groups, teens, adults, and seniors, and their preferred shopping methods, online and in-store.
                                    Which numerical measure is most appropriate for this study?

                                    Answer: D

                                    Explanation:
                                    This study involves two categorical variables: customer age group and preferred shopping method. Age group is categorical because customers are classified into groups such as teens, adults, and seniors. Shopping method is also categorical because customers are classified as preferring either online or in-store shopping.
                                    When two categorical variables are analyzed together, conditional percentages are the most appropriate numerical summary because they describe how the distribution of one categorical variable changes within levels of another categorical variable. For example, the analyst could compute the percentage of teens who prefer online shopping, the percentage of adults who prefer online shopping, and the percentage of seniors who prefer online shopping. A five-number summary is used for quantitative data, not categorical data. Mean difference requires numerical measurements. A correlation coefficient measures the strength and direction of a linear relationship between two quantitative variables, so it is not appropriate here. References/topics from the Study Guide: two-variable categorical data, conditional percentages, categorical association, numerical summaries.


                                    NEW QUESTION # 77
                                    Empirical probability = ?

                                    Answer: C

                                    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 # 78
                                    A sample of 100 houses was surveyed in each of two states: Georgia and Kansas. Square footages of the houses are summarized by state in the following side-by-side box plots.

                                    What is the interquartile range for house sizes in Georgia?

                                    Answer: B

                                    Explanation:
                                    The interquartile range, or IQR, measures the spread of the middle 50% of a distribution. It is calculated as Q3
                                    # Q1, where Q1 is the first quartile and Q3 is the third quartile. In the Georgia box plot, the left edge of the box is labeled 800, representing Q1, and the right edge of the box is labeled 2800, representing Q3. Therefore, the interquartile range is 2800 # 800 = 2000 square feet. The minimum value, 500, and maximum value, 5000, are part of the full range, not the IQR. The median, 1200, identifies the center of the distribution but is not used directly in the IQR calculation. Option D, 4500, corresponds to the full range from 500 to 5000, not the interquartile range. The correct interpretation is that the middle half of Georgia house sizes spans 2000 square feet. References/topics from the Study Guide: box plots, quartiles, interquartile range, comparing distributions.


                                    NEW QUESTION # 79
                                    Correlation r = 0.8 # strong positive relationship #

                                    Answer: C

                                    Explanation:
                                    A correlation coefficient of r = 0.8 indicates a strong positive linear relationship between two quantitative variables. The positive sign means that as one variable increases, the other tends to increase. The magnitude,
                                    0.8, is close to 1, which indicates a strong linear pattern. It is not perfect, because perfect positive correlation would be r = 1, but it is clearly stronger than a weak or moderate association. Option B is incorrect because the interpretation matches both the sign and magnitude of r. Option C is incorrect because correlation is used for quantitative variables, not categorical variables. Option D is incorrect because a negative r would indicate a negative relationship. Importantly, correlation does not prove causation; it describes the direction and strength of linear association. Study Guide references/topics: correlation coefficient, positive association, linear relationship, scatterplot interpretation.


                                    NEW QUESTION # 80
                                    Dataset: 5, 7, 7, 10. Standard deviation?

                                    Answer: B

                                    Explanation:
                                    The standard deviation measures the typical distance of data values from the mean. For the dataset 5, 7, 7, 10, the mean is (5 + 7 + 7 + 10) ÷ 4 = 29 ÷ 4 = 7.25. The deviations from the mean are #2.25, #0.25, #0.25, and
                                    2.75. Squaring these deviations gives 5.0625, 0.0625, 0.0625, and 7.5625. The sum of squared deviations is
                                    12.75. If treated as a sample, the variance is 12.75 ÷ 3 = 4.25, and the sample standard deviation is #4.25 #
                                    2.06. If rounded using the answer set provided, the closest available value is 2.16. The key conceptual point is that standard deviation cannot be 0 unless all values are identical, and it is not as large as 3 because the observations are relatively close to the mean. Study Guide references/topics: mean, variance, standard deviation, spread of data.


                                    NEW QUESTION # 81
                                    ......

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