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

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

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q18-Q23):

                                    NEW QUESTION # 18
                                    Given a normal distribution with a mean of 40 and a standard deviation of 6, what is the range that contains approximately 95% of the data?

                                    Answer: C

                                    Explanation:
                                    For a normal distribution, the empirical rule states that approximately 95% of the data fall within two standard deviations of the mean. The mean is 40, and the standard deviation is 6. Two standard deviations equal 2 × 6
                                    = 12. To construct the 95% interval, subtract and add 12 from the mean: 40 # 12 = 28 and 40 + 12 = 52.
                                    Therefore, the range containing approximately 95% of the data is 28 to 52. Option D, 34 to 46, represents one standard deviation from the mean and corresponds to about 68% of the data. Option B, 22 to 58, represents three standard deviations from the mean and corresponds to approximately 99.7% of the data. Option C is not based on the stated standard deviation. The correct interval must be symmetric around the mean and extend exactly two standard deviations in each direction. References/topics from the Study Guide: normal distribution, empirical rule, mean, standard deviation.


                                    NEW QUESTION # 19
                                    Sum of probabilities in sample space = ?

                                    Answer: D

                                    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 # 20
                                    Empirical probability is based on:

                                    Answer: D

                                    Explanation:
                                    Empirical probability is based on observed data collected from experiments, surveys, simulations, or repeated trials. It is calculated as the relative frequency of an event: number of times the event occurs divided by the total number of trials or observations. For example, if a machine produces 12 defective items in a sample of
                                    300, the empirical probability of a defect is 12/300 = 0.04. This differs from classical or theoretical probability, which is based on equally likely outcomes and mathematical structure, such as a fair die having probability 1/6 for each face. It also differs from subjective probability, which is based on personal judgment or expert belief rather than observed frequency. The word "empirical" signals evidence obtained through observation, so observed frequency is the correct basis. Study Guide references/topics: empirical probability, relative frequency, observed data, probability interpretation.


                                    NEW QUESTION # 21
                                    Which measure of central tendency is least affected by outliers?

                                    Answer: D

                                    Explanation:
                                    The median is the measure of central tendency least affected by outliers because it depends only on the ordered position of values, not on the numerical magnitude of extreme observations. To find the median, the data are arranged from least to greatest and the middle value is identified, or the average of the two middle values is taken when the sample size is even. If an extremely large or extremely small value is added to a data set, the mean can shift substantially because every value contributes to the arithmetic average. The median, however, usually remains stable unless the extreme value changes the middle position. The mode is also not directly affected by magnitude, but it may be absent or non-unique and is often less informative for numerical data. Range is not a measure of central tendency and is highly sensitive to outliers because it uses the minimum and maximum. Study Guide references/topics: descriptive statistics, measures of center, median, resistance to outliers.


                                    NEW QUESTION # 22
                                    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: A

                                    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 # 23
                                    ......

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