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

SectionObjectives
Topic 1: Regression and Correlation- Relationship analysis
  • 1. Simple linear regression basics
    • 2. Correlation coefficient interpretation
      Topic 2: Statistical Inference- Hypothesis testing
      • 1. t-tests and z-tests (basic application)
        • 2. Null and alternative hypotheses
          - Estimation
          • 1. Confidence intervals for means and proportions
            Topic 3: Probability Distributions- Continuous distributions
            • 1. Standard normal and z-scores
              • 2. Normal distribution
                - Discrete distributions
                • 1. Binomial distribution
                  • 2. Poisson distribution (introductory use cases)
                    Topic 4: Descriptive Statistics- Data summarization
                    • 1. Measures of variability (range, variance, standard deviation)
                      • 2. Measures of central tendency (mean, median, mode)
                        - Data visualization
                        • 1. Histograms and frequency distributions
                          • 2. Box plots and interpretation
                            Topic 5: 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

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q60-Q65):

                                    NEW QUESTION # 60
                                    What percent of data lies within 2 standard deviations of the mean in a normal distribution?

                                    Answer: B

                                    Explanation:
                                    For a normal distribution, the empirical rule, also called the 68-95-99.7 rule, describes how data are distributed around the mean. Approximately 68% of observations fall within 1 standard deviation of the mean, approximately 95% fall within 2 standard deviations, and approximately 99.7% fall within 3 standard deviations. The question asks specifically for the percentage within 2 standard deviations, so the correct value is 95%. This interval is written as # # 2# to # + 2#, where # is the mean and # is the standard deviation.
                                    Option B corresponds to one standard deviation, not two. Option C is an imprecise version of the three- standard-deviation rule, and option D has no standard empirical-rule interpretation in this context. This rule is frequently used to estimate ranges in bell-shaped distributions. Study Guide references/topics: normal distribution, empirical rule, standard deviation, distribution spread.


                                    NEW QUESTION # 61
                                    Sum of probabilities in sample space = ?

                                    Answer: A

                                    Explanation:
                                    The probabilities of all outcomes in a complete sample space must sum to 1. A sample space contains every possible outcome of a probability experiment, and one of those outcomes must occur. For example, when rolling a fair six-sided die, the outcomes are 1, 2, 3, 4, 5, and 6. Each has probability 1/6, and the sum is 1/6 +
                                    1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1. A total probability of 0 would mean no outcome can occur, which is impossible for a valid experiment. A total greater than 1 violates probability rules because probabilities cannot exceed certainty. "Cannot exceed 2" is too broad and mathematically invalid, since the exact total must equal
                                    1. This principle is foundational for checking probability distributions and validating whether assigned probabilities are coherent. Study Guide references/topics: sample space, probability axioms, total probability, theoretical probability.


                                    NEW QUESTION # 62
                                    In a normal distribution, 95% of data lies within:

                                    Answer: C

                                    Explanation:
                                    For a normal distribution, the empirical rule states that approximately 68% of data fall within one standard deviation of the mean, approximately 95% fall within two standard deviations, and approximately 99.7% fall within three standard deviations. The notation ±2 SD means two standard deviations below the mean to two standard deviations above the mean, or # # 2# to # + 2#. Therefore, the interval containing about 95% of normally distributed observations is ±2 standard deviations. Option B corresponds to approximately 68%, not
                                    95%. Option C corresponds to approximately 99.7%, and option D extends beyond the standard empirical- rule benchmarks. This concept is central when estimating the typical spread of bell-shaped data, such as test scores, biological measurements, or repeated measurement errors. The correct answer is ±2 SD because it matches the 95% portion of the 68-95-99.7 rule. Study Guide references/topics: normal distribution, empirical rule, standard deviation, distribution spread.


                                    NEW QUESTION # 63
                                    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 # 64
                                    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 # 65
                                    ......

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