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

SectionObjectives
Topic 1: Regression and Modeling- Linear Relationships
  • 1. Slope and intercept interpretation
    • 2. Simple linear regression
      Topic 2: Descriptive Statistics- Single Variable Data Analysis
      • 1. Measures of dispersion (variance, standard deviation, range)
        • 2. Measures of central tendency (mean, median, mode)
          • 3. Data visualization (histograms, box plots)
            - Two Variable Data Analysis
            • 1. Outliers and relationships
              • 2. Scatter plots interpretation
                • 3. Correlation
                  Topic 3: Probability Theory- Fundamental Probability Concepts
                  • 1. Independent vs dependent events
                    • 2. Basic probability rules
                      • 3. Conditional probability
                        - Probability Distributions
                        • 1. Binomial distribution basics
                          • 2. Normal distribution
                            Topic 4: Statistical Inference- Estimation and Confidence Intervals
                            • 1. Confidence interval interpretation
                              • 2. Point estimates
                                - Hypothesis Testing (Introductory Level)
                                • 1. Null vs alternative hypothesis
                                  • 2. p-values interpretation

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q114-Q119):

                                    NEW QUESTION # 114
                                    Determine x:
                                    4 + x = 6 # x

                                    Answer: B

                                    Explanation:
                                    The equation 4 + x = 6 # x is a linear equation in one variable. To solve it, collect variable terms on one side and constant terms on the other. Add x to both sides to eliminate the negative x on the right: 4 + 2x = 6. Then subtract 4 from both sides: 2x = 2. Finally, divide both sides by 2, giving x = 1. This value can be verified directly in the original equation. Substituting x = 1 gives 4 + 1 = 5 on the left and 6 # 1 = 5 on the right, so both sides are equal. Option A gives 4 = 6, which is false. Option C gives 6 = 4, also false. Option D gives 9 =
                                    1, which is not valid. The correct solution is the value that balances both sides of the equation. References
                                    /topics from the Study Guide: basic algebra, solving linear equations, inverse operations, substitution checks.


                                    NEW QUESTION # 115
                                    A teacher plots the test scores of a class using the box plot.

                                    What is true about the test scores?

                                    Answer: D

                                    Explanation:
                                    A box plot displays the five-number summary of a quantitative data set: minimum, first quartile, median, third quartile, and maximum. The median is represented by the vertical line inside the box. In the given box plot, that internal vertical line is positioned at 80 on the score axis. Therefore, the median test score for Class A is
                                    80 points. The value 70 corresponds to the left edge of the box, which represents the first quartile, not the median. The value near 88 represents the right edge of the box, which is the third quartile. The whiskers extend to the approximate minimum and maximum scores, but those values do not determine the median. The median divides the ordered data into two equal halves, meaning about 50% of the students scored at or below
                                    80 and about 50% scored at or above 80. References/topics from the Study Guide: box plots, five-number summary, median, quartiles.


                                    NEW QUESTION # 116
                                    Probability of rolling 1, 2, or 3 on die = ?

                                    Answer: B

                                    Explanation:
                                    A standard six-sided die has six equally likely outcomes: 1, 2, 3, 4, 5, and 6. The event "rolling 1, 2, or 3" has three favorable outcomes: 1, 2, and 3. The probability is therefore favorable outcomes divided by total outcomes: 3/6. This fraction simplifies to 1/2. Option B, 1/3, would correspond to two favorable outcomes out of six. Option C, 1/6, is the probability of rolling one specific number only. Option D, 2/3, would require four favorable outcomes out of six. Since exactly half of the die faces are 1, 2, or 3, the correct probability is one- half. This is a direct application of theoretical probability with equally likely outcomes. Study Guide references/topics: die probability, favorable outcomes, sample space, theoretical probability.


                                    NEW QUESTION # 117
                                    95% CI = 50 ± 2. SE = ?

                                    Answer: C

                                    Explanation:
                                    A confidence interval has the structure estimate ± margin of error. The margin of error is calculated as critical value × standard error. For a 95% confidence interval using the normal approximation, the critical value is approximately 1.96, often rounded to 2 in introductory settings. The interval is given as 50 ± 2, so the margin of error is 2. Using the approximate 95% critical value of 2, we solve 2 = 2 × SE, giving SE = 1. More exactly, using 1.96 gives SE = 2/1.96 # 1.02, which rounds to 1. Option B confuses the margin of error with the standard error. Option C is too large, and option D would produce a margin of error near 1 under a 95% critical value. The correct standard error is approximately 1. Study Guide references/topics: confidence intervals, standard error, critical value, margin of error.


                                    NEW QUESTION # 118
                                    Two independent events: P(A and B) = ?

                                    Answer: B

                                    Explanation:
                                    For independent events, the probability that both events occur is the product of their individual probabilities.
                                    The rule is P(A and B) = P(A) × P(B). Independence means that the occurrence of one event does not change the probability of the other. For example, if a coin is tossed and a die is rolled, the probability of heads and rolling a 4 is 1/2 × 1/6 = 1/12. Option B is an addition expression used in "or" problems, not "and" problems.
                                    Option C applies to mutually exclusive events, not independent events. Option D would mean both events are certain to occur together, which is not generally true. The word "and" signals intersection, and independence allows the intersection to be calculated by multiplication. Study Guide references/topics: independent events, multiplication rule, joint probability, compound probability.


                                    NEW QUESTION # 119
                                    ......

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