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

SectionObjectives
Topic 1: Regression and Modeling- Linear Relationships
  • 1. Simple linear regression
    • 2. Slope and intercept interpretation
      Topic 2: Probability Theory- Fundamental Probability Concepts
      • 1. Independent vs dependent events
        • 2. Basic probability rules
          • 3. Conditional probability
            - Probability Distributions
            • 1. Normal distribution
              • 2. Binomial distribution basics
                Topic 3: 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. Scatter plots interpretation
                        • 2. Outliers and relationships
                          • 3. Correlation
                            Topic 4: 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

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                                    Best WGU Applied-Probability-and-Statistics exam questions and answers

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q55-Q60):

                                    NEW QUESTION # 55
                                    Random variable X = number of heads in 4 coin flips #

                                    Answer: D

                                    Explanation:
                                    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.


                                    NEW QUESTION # 56
                                    Independent events: P(A|B) = ?

                                    Answer: C

                                    Explanation:
                                    For independent events, the occurrence of one event does not change the probability of the other. Conditional probability P(A|B) means the probability of A occurring given that B has occurred. If A and B are independent, knowing B occurred gives no new information about A. Therefore, P(A|B) = P(A). This is one of the defining properties of independence. For example, if a coin toss and a die roll are independent, knowing the die landed on 4 does not change the probability that the coin landed heads; it remains 1/2. Option B reverses the event being measured. Option C would imply that A becomes impossible after B, which describes a different situation. Option D is an addition expression and does not represent conditional probability. The correct relationship is that the conditional probability equals the original probability when events are independent. Study Guide references/topics: independent events, conditional probability, probability rules, event relationships.


                                    NEW QUESTION # 57
                                    A hospital analyzes the recovery rates of patients undergoing two different treatments for a specific condition.
                                    Treatment X has an overall recovery rate of 80%, while Treatment Y has a recovery rate of 90%. However, when the data is divided by age groups, Treatment X has a higher recovery rate in each age group compared to Treatment Y.
                                    Is Simpson's paradox present in this study?

                                    Answer: A

                                    Explanation:
                                    Simpson's paradox occurs when an association observed in aggregated data reverses or conflicts with the association observed within relevant subgroups. In this case, the overall recovery rate appears better for Treatment Y, since Y has a 90% overall recovery rate compared with 80% for Treatment X. However, after the data are divided by age group, Treatment X has a higher recovery rate in every age group. That reversal between the overall comparison and the subgroup comparisons is precisely the defining structure of Simpson' s paradox. Age group functions as the lurking or confounding variable because different age distributions across treatment groups can distort the overall recovery rates. Option B states a true overall fact, but it ignores the contradiction created by the age-specific rates. Option C is too general; simple differences between treatments do not necessarily create Simpson's paradox. The key issue is inconsistency between aggregate and stratified results. References/topics from the Study Guide: two-variable data, confounding variables, conditional comparisons, Simpson's paradox.


                                    NEW QUESTION # 58
                                    What is the mode of this dataset: 3, 5, 7, 7, 10?

                                    Answer: C

                                    Explanation:
                                    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.


                                    NEW QUESTION # 59
                                    Correlation coefficient r = #0.5 #

                                    Answer: B

                                    Explanation:
                                    The correlation coefficient r describes the direction and strength of a linear relationship between two quantitative variables. Its values range from #1 to +1. A negative value indicates that as one variable increases, the other tends to decrease. Since r = #0.5, the direction is negative. Its magnitude, 0.5, is not close enough to zero to indicate no relationship, but it is also not close enough to #1 to represent an extremely strong relationship. Therefore, the best description is a moderate negative linear relationship. Option B is incorrect because the sign is negative, not positive. Option C is incorrect for both direction and strength.
                                    Option D would be appropriate only when r is near 0, indicating little or no linear association. A scatterplot with r = #0.5 would generally show a downward trend, but with noticeable scatter around the trend. Study Guide references/topics: correlation coefficient, negative association, scatterplots, linear relationship strength.


                                    NEW QUESTION # 60
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