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

SectionObjectives
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. Outliers and relationships
            • 3. Scatter plots interpretation
              Probability Theory- Fundamental Probability Concepts
              • 1. Basic probability rules
                • 2. Conditional probability
                  • 3. Independent vs dependent events
                    - Probability Distributions
                    • 1. Binomial distribution basics
                      • 2. Normal distribution
                        Statistical Inference- Hypothesis Testing (Introductory Level)
                        • 1. Null vs alternative hypothesis
                          • 2. p-values interpretation
                            - Estimation and Confidence Intervals
                            • 1. Confidence interval interpretation
                              • 2. Point estimates
                                Regression and Modeling- Linear Relationships
                                • 1. Slope and intercept interpretation
                                  • 2. Simple linear regression

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q40-Q45):

                                    NEW QUESTION # 40
                                    Poisson distribution mean = ?

                                    Answer: C

                                    Explanation:
                                    For a Poisson distribution, the mean is #, pronounced "lambda." The parameter # represents the expected number of events occurring in a fixed interval, such as calls per hour, defects per batch, or arrivals per minute.
                                    A defining feature of the Poisson distribution is that both the mean and variance are equal to #. Therefore, if X follows a Poisson distribution with # = 4, then the expected value, or mean, is 4, and the variance is also 4.
                                    Option B and option C are only correct in special cases where # happens to equal 0 or 1, not generally. Option D is conceptually related because the Poisson variance equals #, but the question asks for the mean, and the parameter name is #. The Poisson distribution is used for discrete counts of events over a fixed interval under a constant average rate. Study Guide references/topics: Poisson distribution, expected value, variance, # parameter.


                                    NEW QUESTION # 41
                                    Dataset: 3, 5, 7, 9, 11. Median = ?

                                    Answer: A

                                    Explanation:
                                    The median is the center value of an ordered dataset. The values 3, 5, 7, 9, and 11 are already arranged from least to greatest. Because there are five observations, the median is the third value, with two observations below it and two observations above it. The third value is 7, so the median is 7. The median is a measure of central tendency that describes the middle position of the data rather than the arithmetic average. In this dataset, the mean is also 7 because the values are evenly spaced around 7, but the median is determined by position, not by summing and dividing. Option B is the second value, option C is the fourth value, and option D is not a data value. The correct answer is the value that splits the ordered list into two equal halves. Study Guide references/topics: median, ordered data, measures of center, descriptive statistics.


                                    NEW QUESTION # 42
                                    Probability of rolling an odd number on a die:

                                    Answer: C

                                    Explanation:
                                    A standard six-sided die has six equally likely outcomes: 1, 2, 3, 4, 5, and 6. The odd outcomes are 1, 3, and
                                    5. Thus, there are 3 favorable outcomes out of 6 possible outcomes. The probability is 3/6, which simplifies to
                                    1/2. This means an odd number is just as likely as an even number on a fair die. Option B, 1/3, would represent 2 favorable outcomes out of 6, which is not correct. Option C, 1/6, is the probability of rolling one specific number, such as only a 1. Option D, 2/3, would require 4 favorable outcomes out of 6. Since exactly half the faces are odd, the probability is one-half. Study Guide references/topics: theoretical probability, equally likely outcomes, sample space, favorable outcomes.


                                    NEW QUESTION # 43
                                    A cafe recorded the total ice cream sales and the average maximum temperature of the day. The scatterplot shows the recorded data. The regression equation y = 13x # 598 estimates the total ice cream sales, y, of a day and the average maximum temperature, x, on that day.

                                    What does the slope represent in this context?

                                    Answer: D

                                    Explanation:
                                    In a linear regression equation of the form y = mx + b, the slope m gives the predicted change in the response variable y for a one-unit increase in the explanatory variable x. Here, y represents total ice cream sales and x represents average maximum temperature. The equation y = 13x # 598 has slope 13, so the model predicts that ice cream sales increase by about $13 for every 1°F increase in temperature. This is not the sales value at
                                    0°F; that would be the intercept, #598, which is generally not meaningful in this practical context. It is also not the predicted sales at 100°F, because that would require substituting x = 100 into the regression equation.
                                    The positive slope matches the upward trend in the scatterplot: higher temperatures are associated with higher ice cream sales. References/topics from the Study Guide: correlation and regression, slope interpretation, explanatory and response variables.


                                    NEW QUESTION # 44
                                    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 # 45
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