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

SectionObjectives
Regression and Correlation- Relationship analysis
  • 1. Correlation coefficient interpretation
    • 2. Simple linear regression basics
      Descriptive Statistics- Data summarization
      • 1. Measures of variability (range, variance, standard deviation)
        • 2. Measures of central tendency (mean, median, mode)
          - Data visualization
          • 1. Box plots and interpretation
            • 2. Histograms and frequency distributions
              Probability Distributions- Discrete distributions
              • 1. Binomial distribution
                • 2. Poisson distribution (introductory use cases)
                  - Continuous distributions
                  • 1. Normal distribution
                    • 2. Standard normal and z-scores
                      Statistical Inference- Estimation
                      • 1. Confidence intervals for means and proportions
                        - Hypothesis testing
                        • 1. t-tests and z-tests (basic application)
                          • 2. Null and alternative hypotheses
                            Probability- Probability rules
                            • 1. Bayes’ theorem (introductory level)
                              • 2. Addition and multiplication rules
                                - Fundamental probability concepts
                                • 1. Conditional probability and independence
                                  • 2. Events and sample spaces

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q14-Q19):

                                    NEW QUESTION # 14
                                    In a standard normal distribution, z-score for the mean = ?

                                    Answer: D

                                    Explanation:
                                    A z-score measures how many standard deviations a value is above or below the mean. The formula is z = (x
                                    # #) / #, where x is the observed value, # is the mean, and # is the standard deviation. If the observed value equals the mean, then x = #. Substituting into the formula gives z = (# # #) / # = 0 / # = 0. Therefore, the z- score corresponding to the mean is always 0 in any normal distribution, including the standard normal distribution. In the standard normal distribution specifically, the mean is 0 and the standard deviation is 1, so the mean lies exactly at z = 0. A z-score of 1 would indicate one standard deviation above the mean, and #1 would indicate one standard deviation below the mean. Study Guide references/topics: standard normal distribution, z-scores, mean, standard deviation.


                                    NEW QUESTION # 15
                                    Z-score negative #

                                    Answer: A

                                    Explanation:
                                    A z-score measures how many standard deviations a data value is from the mean. The formula is z = (x # #)/#, where x is the observed value, # is the mean, and # is the standard deviation. Since standard deviation is positive, the sign of the z-score depends on the numerator, x # #. If x is less than the mean, then x # # is negative, producing a negative z-score. Therefore, a negative z-score indicates that the observed value is below the mean. A positive z-score indicates a value above the mean, while a z-score of 0 indicates a value exactly equal to the mean. Option D is incorrect because the sign of the z-score gives direct positional information relative to the mean. Study Guide references/topics: z-scores, standard normal distribution, mean, standard deviation.


                                    NEW QUESTION # 16
                                    Which graph displays data in a manner that is accurate?



                                    Answer: D

                                    Explanation:
                                    The accurate display is the bar graph labeled "Number of Feet Traveled" with the vertical axis showing the number of feet and the horizontal axis identifying the student travelers. For discrete observations associated with individual students, a bar graph is appropriate because each bar represents a separate category or individual and its height represents the measured value. Option A is inaccurate because its title states
                                    "Number of Miles Traveled," while the vertical axis is labeled in feet; this creates a unit mismatch. Option C uses a pie chart, which is designed to show parts of a whole, not individual measured distances unless the goal is proportional composition. Option D uses a line graph, which is typically reserved for ordered change, especially over time; connecting student traveler values implies continuity or trend that is not justified. The correct graph must use consistent units, clear labels, and an appropriate display type. References/topics from the Study Guide: data displays, bar graphs, categorical identifiers, quantitative measurements, graph accuracy.


                                    NEW QUESTION # 17
                                    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: B


                                    NEW QUESTION # 18
                                    A child's parents want to analyze the relationship between the daily high temperature and ice cream sales at their child's ice cream stand. They create the following scatterplot.

                                    What is the estimated value of r, the correlation coefficient, between these variables?

                                    Answer: B

                                    Explanation:
                                    The correlation coefficient r measures both the direction and strength of a linear relationship between two quantitative variables. In this scatterplot, the points rise from lower left to upper right, showing a positive association between temperature and daily ice cream sales. As temperature increases, sales also tend to increase. The points are fairly close to an upward-sloping linear pattern, so the relationship is strong rather than weak. A value of r near 1 indicates a strong positive linear association, while a value near #1 indicates a strong negative association. Since the association is clearly positive, the negative options, #0.93 and #0.39, are not appropriate. Since the points show a strong trend rather than a loose or weak trend, 0.39 is too small.
                                    The best estimate is 0.93. This is consistent with the visual pattern: temperature explains a substantial amount of the linear movement in ice cream sales. References/topics from the Study Guide: scatterplots, correlation coefficient, positive association, strength of linear relationship.


                                    NEW QUESTION # 19
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