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

SectionObjectives
Topic 1: Statistical Inference- Estimation
  • 1. Confidence intervals for means and proportions
    - Hypothesis testing
    • 1. Null and alternative hypotheses
      • 2. t-tests and z-tests (basic application)
        Topic 2: Probability Distributions- Continuous distributions
        • 1. Standard normal and z-scores
          • 2. Normal distribution
            - Discrete distributions
            • 1. Poisson distribution (introductory use cases)
              • 2. Binomial distribution
                Topic 3: Regression and Correlation- Relationship analysis
                • 1. Correlation coefficient interpretation
                  • 2. Simple linear regression basics
                    Topic 4: Probability- Probability rules
                    • 1. Bayes’ theorem (introductory level)
                      • 2. Addition and multiplication rules
                        - Fundamental probability concepts
                        • 1. Events and sample spaces
                          • 2. Conditional probability and independence
                            Topic 5: 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)

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q84-Q89):

                                    NEW QUESTION # 84
                                    The dot plot illustrates the frequency of outdoor games played by students per week.

                                    Which statement is true?

                                    Answer: C

                                    Explanation:
                                    The dot plot shows a distribution centered near 3 days, with substantial frequencies at 2, 3, and 4 days and smaller frequencies at the extremes of 1 and 5 days. This shape is reasonably balanced around the center.
                                    When a distribution is approximately symmetric, the mean and median tend to be close because the lower and higher values balance each other. The median identifies the middle observation after the data are ordered, and the mean represents the balance point of the distribution. Since the tallest stack is near 3 days and the surrounding stacks on 2 and 4 days are comparable, the center of the data is approximately 3 days by both measures. There is no strong skew to pull the mean far above or below the median. Therefore, the best statement is that the mean is almost the same as the median. Options B and C would require clear skew or extreme imbalance, which the dot plot does not show. References/topics from the Study Guide: dot plots, mean, median, distribution shape, symmetry.


                                    NEW QUESTION # 85
                                    Expected value of X = 1×0.2 + 2×0.5 + 3×0.3 = ?

                                    Answer: A

                                    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 # 86
                                    There are 20 men in a room whose heights are reflected in inches as 68, 70, 73, 67, 71, 68, 76, 70, 73, 66, 68,
                                    69, 71, 74, 73, 72, 65, 60, 70, and 78 inches respectively.
                                    What is the median of these data?

                                    Answer: A

                                    Explanation:
                                    The median is the middle value of an ordered data set. Because there are 20 observations, the number of data values is even, so the median is the average of the 10th and 11th values after the data are arranged from least to greatest. Ordering the heights gives 60, 65, 66, 67, 68, 68, 68, 69, 70, 70, 70, 71, 71, 72, 73, 73, 73, 74, 76,
                                    78. The 10th value is 70, and the 11th value is also 70. The median is therefore (70 + 70) ÷ 2 = 70. This value divides the ordered heights into two equal halves: ten values are at or below 70, and ten values are at or above
                                    70. The median is resistant to extreme values, so the low value 60 and the high value 78 do not distort it the way they could affect the mean. References/topics from the Study Guide: median, ordered data, measures of center, quantitative data.


                                    NEW QUESTION # 87
                                    Variance of Poisson # = 5 = ?

                                    Answer: A

                                    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 # 88
                                    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: C

                                    Explanation:
                                    This experiment has two independent stages: tossing a coin and spinning a numbered spinner. The probability of getting heads on a fair coin is 1/2. The spinner has 8 equally likely outcomes numbered 1 through 8. A number less than 3 means either 1 or 2, so there are 2 favorable spinner outcomes out of 8 total outcomes.
                                    Thus, P(number less than 3) = 2/8 = 1/4. Since the coin result does not affect the spinner result, the events are independent. For independent events connected by "and," multiply the probabilities: 1/2 × 1/4 = 1/8.
                                    Equivalently, the combined sample space has 2 coin outcomes times 8 spinner outcomes, or 16 total equally likely outcomes. The favorable outcomes are heads with 1 and heads with 2, giving 2/16 = 1/8. References
                                    /topics from the Study Guide: independent events, sample spaces, multiplication rule, theoretical probability.


                                    NEW QUESTION # 89
                                    ......

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