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

SectionObjectives
Topic 1: Descriptive Statistics- Data visualization
  • 1. Histograms and frequency distributions
    • 2. Box plots and interpretation
      - Data summarization
      • 1. Measures of variability (range, variance, standard deviation)
        • 2. Measures of central tendency (mean, median, mode)
          Topic 2: 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
                Topic 3: Probability Distributions- Discrete distributions
                • 1. Binomial distribution
                  • 2. Poisson distribution (introductory use cases)
                    - Continuous distributions
                    • 1. Standard normal and z-scores
                      • 2. Normal distribution
                        Topic 4: Probability- Probability rules
                        • 1. Addition and multiplication rules
                          • 2. Bayes’ theorem (introductory level)
                            - Fundamental probability concepts
                            • 1. Events and sample spaces
                              • 2. Conditional probability and independence
                                Topic 5: Regression and Correlation- Relationship analysis
                                • 1. Simple linear regression basics
                                  • 2. Correlation coefficient interpretation

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q130-Q135):

                                    NEW QUESTION # 130
                                    Variance of Poisson # = 5 = ?

                                    Answer: D

                                    Explanation:
                                    A defining property of the Poisson distribution is that its variance equals its mean, and both are equal to #.
                                    Since the question states # = 5, the variance is also 5. This property distinguishes the Poisson distribution from many other probability distributions. The mean represents the expected number of events per interval, while the variance describes the spread of the event count around that mean. In a Poisson model with # = 5, event counts tend to vary around 5, and the numerical variance is 5. Option B, 4, option C, 0, and option D, 1, do not follow from the Poisson variance rule. The result is not obtained by squaring # or taking its square root; it is simply equal to #. Study Guide references/topics: Poisson distribution, variance, mean, # parameter.


                                    NEW QUESTION # 131
                                    Expected value of X = 1×0.2 + 2×0.5 + 3×0.3 = ?

                                    Answer: B

                                    Explanation:
                                    Expected value is the long-run average value of a random variable. For a discrete random variable, it is calculated by multiplying each possible value by its probability and then adding those products. Here, the expression is already structured as an expected value calculation: 1×0.2 + 2×0.5 + 3×0.3. Compute each product: 1×0.2 = 0.2, 2×0.5 = 1.0, and 3×0.3 = 0.9. Add them: 0.2 + 1.0 + 0.9 = 2.1. Therefore, the expected value is 2.1. This does not mean the random variable must equal 2.1 in a single trial; it means that over many repetitions, the average outcome would approach 2.1. Option B is close but omits part of the weighted contribution. Options C and D do not match the weighted-average computation. Study Guide references
                                    /topics: expected value, discrete random variables, weighted average, probability distributions.


                                    NEW QUESTION # 132
                                    Review the following inequality:
                                    y < x # 1/2
                                    Which shaded portion in the graphs corresponds to this inequality?



                                    Answer: A

                                    Explanation:
                                    The inequality y < x # 1/2 has boundary line y = x # 1/2. This line has slope 1 and y-intercept #1/2, so it crosses the y-axis slightly below the origin and rises one unit for every one unit moved to the right. Because the inequality is strict, using " < " rather than "#," the boundary line must be dashed, showing that points on the line are not included in the solution set. The solution region must be shaded below the line because y is less than the expression x # 1/2. A useful verification method is the test point (0, 0). Substituting gives 0 < 0 #
                                    1/2, or 0 < #1/2, which is false. Therefore, the region containing the origin should not be shaded. The fourth graph has the dashed boundary with intercept #1/2 and shades the region below the line while excluding the origin. References/topics from the Study Guide: graphing linear inequalities, slope-intercept form, dashed boundaries, test-point method.


                                    NEW QUESTION # 133
                                    Binomial distribution parameters = ?

                                    Answer: D

                                    Explanation:
                                    A binomial distribution is defined by two parameters: n and p. The parameter n is the fixed number of trials, and p is the probability of success on each trial. The model applies when trials are independent, each trial has two possible outcomes, and p remains constant. For example, if X is the number of heads in 10 fair coin flips, then X follows a binomial distribution with n = 10 and p = 0.5. Option B, #, is the parameter of a Poisson distribution, used for counts of events over intervals. Option C, # and #, commonly describes a normal distribution, where # is the mean and # is the standard deviation. Option D is incorrect because the binomial model has a precise parameter structure. Identifying n and p is essential before calculating binomial probabilities or expected value. Study Guide references/topics: binomial distribution, independent trials, success probability, discrete probability.


                                    NEW QUESTION # 134
                                    Standard error decreases when:

                                    Answer: C

                                    Explanation:
                                    The standard error of the sample mean is calculated as SE = s/#n, where s is the sample standard deviation and n is the sample size. Since n appears in the denominator, increasing the sample size reduces the standard error, assuming the standard deviation stays constant. This reflects the fact that larger samples produce more stable estimates of the population mean. Option B is incorrect because decreasing sample size increases standard error. Option C is incorrect because a larger standard deviation increases standard error by increasing the numerator. Option D is incorrect because the mean affects the center of the distribution but does not directly determine the standard error. Standard error is about precision: smaller standard error means less sampling variability and a more precise estimate. That is why larger samples are preferred in inference. Study Guide references/topics: standard error, sample size, standard deviation, sampling variability.


                                    NEW QUESTION # 135
                                    ......

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