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

SectionObjectives
Probability- Fundamental probability concepts
  • 1. Events and sample spaces
    • 2. Conditional probability and independence
      - Probability rules
      • 1. Bayes’ theorem (introductory level)
        • 2. Addition and multiplication rules
          Statistical Inference- Hypothesis testing
          • 1. Null and alternative hypotheses
            • 2. t-tests and z-tests (basic application)
              - Estimation
              • 1. Confidence intervals for means and proportions
                Regression and Correlation- Relationship analysis
                • 1. Simple linear regression basics
                  • 2. Correlation coefficient interpretation
                    Probability Distributions- Continuous distributions
                    • 1. Standard normal and z-scores
                      • 2. Normal distribution
                        - 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 (FZO1 C955) Sample Questions (Q31-Q36):

                                    NEW QUESTION # 31
                                    Probability it does NOT rain = 1 # 0.25 = ?

                                    Answer: B

                                    Explanation:
                                    This question uses the complement rule of probability. If the probability that it rains is 0.25, then the probability that it does not rain is the complement of that event. The complement rule states that P(not A) = 1
                                    # P(A). Here, A represents the event "it rains," so P(not rain) = 1 # 0.25 = 0.75. This means there is a 75% probability that rain does not occur. Option B repeats the probability of rain rather than its complement.
                                    Option C would imply rain and no rain are equally likely, which is not supported by the given probability.
                                    Option D would mean no rain is certain, but a 0.25 probability of rain means rain is still possible. The key technical point is that an event and its complement must sum to 1. Study Guide references/topics: probability, complement rule, event probability, sample-space total.


                                    NEW QUESTION # 32
                                    The average commute time for workers in a city in 2021 was 35 minutes, with a standard deviation of 5 minutes.
                                    Assuming a normal distribution, which two values encompass 95% of the data?

                                    Answer: A

                                    Explanation:
                                    For a normally distributed variable, the empirical rule states that approximately 95% of observations fall within two standard deviations of the mean. The mean commute time is 35 minutes, and the standard deviation is 5 minutes. Two standard deviations equal 2 × 5 = 10 minutes. Therefore, the interval covering approximately 95% of the data is 35 # 10 to 35 + 10, which gives 25 minutes to 45 minutes. Option B, 30 to
                                    40 minutes, represents only one standard deviation from the mean and would cover approximately 68% of the data, not 95%. Option A extends three standard deviations from the mean and would correspond to roughly
                                    99.7% under the empirical rule. Option D is not centered properly around the mean and does not represent a standard normal interval. The correct interval is symmetric about the mean and uses the standard deviation as the spread measure. References/topics from the Study Guide: normal distribution, empirical rule, mean, standard deviation.


                                    NEW QUESTION # 33
                                    Regression intercept represents:

                                    Answer: B

                                    Explanation:
                                    In a linear regression equation, usually written as # = b# + b#x, the intercept b# represents the predicted value of Y when X equals 0. It is the point where the regression line crosses the vertical axis. For example, if a model is # = 12 + 3x, the intercept 12 means the predicted response is 12 when x = 0. The slope, b#, is different; it represents the predicted change in Y for each one-unit increase in X. Correlation measures the strength and direction of a linear association, not the intercept. The mean is a measure of center for a variable and is not the same as a regression intercept. In applied settings, the intercept is meaningful only when X = 0 is within a realistic or relevant range of the data. Study Guide references/topics: linear regression, intercept interpretation, slope-intercept form, response prediction.


                                    NEW QUESTION # 34
                                    A home inspector finds 3% of the homes in a community infected with termites.
                                    How should the home inspector's findings be interpreted?

                                    Answer: B

                                    Explanation:
                                    A probability or percentage describes how often an event is expected to occur in the long run. Here, 3% of homes are infected with termites. As a probability, this is 0.03, meaning about 3 out of every 100 homes would be expected to have termites. This is a small probability, so the event should be interpreted as unlikely.
                                    It is not impossible, because impossible would require a probability of 0%. It is also not likely, because likely events generally have probabilities substantially greater than 50%. Finally, it is not "as likely as unlikely," because that language corresponds to a probability near 50%, where occurrence and nonoccurrence are approximately balanced. Since 3% is close to zero but not equal to zero, the technically correct interpretation is that termite infection is unlikely for a randomly selected home in the community. References/topics from the Study Guide: probability interpretation, percentages, unlikely events, complementary probability.


                                    NEW QUESTION # 35
                                    Determine z in the equation:
                                    1/(6z) = 2/9

                                    Answer: B

                                    Explanation:
                                    The equation 1/(6z) = 2/9 is a proportion because it sets two fractions equal to each other. To solve it, use cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction, and multiply the denominator of the first fraction by the numerator of the second fraction: 1 × 9 = 2 × 6z. This gives 9 = 12z. To isolate z, divide both sides by 12: z = 9/12. This fraction can also be simplified to 3/4, but the answer choices list the unsimplified equivalent form 9/12. The other options do not satisfy the original equation. For example, if z = 2/54, then 6z is very small and the left side becomes much larger than 2/9. If z =
                                    12/9 or 18/2, the denominator becomes too large, making the left side too small. References/topics from the Study Guide: proportions, solving equations, cross multiplication, equivalent fractions.


                                    NEW QUESTION # 36
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