Applied-Probability-and-Statistics Exam Material | Applied-Probability-and-Statistics Dumps Download

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

SectionObjectives
Statistical Inference- Estimation and Confidence Intervals
  • 1. Confidence interval interpretation
    • 2. Point estimates
      - Hypothesis Testing (Introductory Level)
      • 1. p-values interpretation
        • 2. Null vs alternative hypothesis
          Descriptive Statistics- 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)
                - Two Variable Data Analysis
                • 1. Correlation
                  • 2. Outliers and relationships
                    • 3. Scatter plots interpretation
                      Regression and Modeling- Linear Relationships
                      • 1. Simple linear regression
                        • 2. Slope and intercept interpretation
                          Probability Theory- Fundamental Probability Concepts
                          • 1. Conditional probability
                            • 2. Independent vs dependent events
                              • 3. Basic probability rules
                                - Probability Distributions
                                • 1. Normal distribution
                                  • 2. Binomial distribution basics

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q119-Q124):

                                    NEW QUESTION # 119
                                    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 # 120
                                    In a standard normal distribution, z-score for the mean = ?

                                    Answer: D

                                    Explanation:
                                    A z-score measures how many standard deviations a value is above or below the mean. The formula is z = (x
                                    # #) / #, where x is the observed value, # is the mean, and # is the standard deviation. If the observed value equals the mean, then x = #. Substituting into the formula gives z = (# # #) / # = 0 / # = 0. Therefore, the z- score corresponding to the mean is always 0 in any normal distribution, including the standard normal distribution. In the standard normal distribution specifically, the mean is 0 and the standard deviation is 1, so the mean lies exactly at z = 0. A z-score of 1 would indicate one standard deviation above the mean, and #1 would indicate one standard deviation below the mean. Study Guide references/topics: standard normal distribution, z-scores, mean, standard deviation.


                                    NEW QUESTION # 121
                                    t-test used when:

                                    Answer: C

                                    Explanation:
                                    A t-test is used when making inferences about a population mean and the population standard deviation, #, is unknown. In practical settings, # is rarely available, so the sample standard deviation, s, is used as an estimate.
                                    That substitution introduces additional uncertainty, which is why the t-distribution is used instead of the standard normal distribution. The t-distribution has heavier tails, especially for small samples, reflecting the extra variability caused by estimating # from the sample. Option B describes a z-test setting, where the population standard deviation is known. Option C is incorrect because categorical population data are usually analyzed with proportions, chi-square tests, or related categorical procedures, not mean-based t-tests. Option D is invalid because t-tests have a clear inferential role. The controlling condition is unknown #, with inference focused on means. Study Guide references/topics: t-tests, unknown population standard deviation, sample standard deviation, inferential statistics.


                                    NEW QUESTION # 122
                                    A dataset: 2, 4, 6, 8, 10. Variance = ?

                                    Answer: C

                                    Explanation:
                                    Variance measures the average squared distance of data values from the mean. For the dataset 2, 4, 6, 8, 10, the mean is (2 + 4 + 6 + 8 + 10) ÷ 5 = 30 ÷ 5 = 6. The deviations from the mean are #4, #2, 0, 2, and 4.
                                    Squaring these deviations gives 16, 4, 0, 4, and 16. The sum of squared deviations is 40. Using the sample variance formula, divide by n # 1, where n = 5. Thus, sample variance = 40 ÷ 4 = 10. Option A is correct.
                                    Option C, 6.25, does not result from the standard sample variance computation for these values. The important distinction is whether a problem is using sample variance or population variance; the provided answer set and calculation use the sample variance formula. Study Guide references/topics: variance, mean, squared deviations, sample variance.


                                    NEW QUESTION # 123
                                    Expected value = ?

                                    Answer: B

                                    Explanation:
                                    Expected value is the theoretical long-term average outcome of a random variable over many repeated trials.
                                    It is calculated by multiplying each possible value by its probability and then summing those products. For a discrete random variable, E(X) = #xP(x). Expected value does not necessarily have to be an outcome that can occur in one trial. For example, the expected value of rolling a fair six-sided die is 3.5, even though no face shows 3.5. It represents the balance point of the probability distribution. The median is the middle value of an ordered distribution, and the mode is the most likely or most frequent value. Expected value may equal 0 in some distributions, but it is not defined as 0. The best conceptual definition is long-term average. Study Guide references/topics: expected value, random variables, probability distributions, long-run average.


                                    NEW QUESTION # 124
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