Applied-Probability-and-Statistics Exam Format, Pass Applied-Probability-and-Statistics Rate

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

SectionObjectives
Descriptive Statistics- Two Variable Data Analysis
  • 1. Correlation
    • 2. Scatter plots interpretation
      • 3. Outliers and relationships
        - 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)
              Probability Theory- Probability Distributions
              • 1. Normal distribution
                • 2. Binomial distribution basics
                  - Fundamental Probability Concepts
                  • 1. Basic probability rules
                    • 2. Conditional probability
                      • 3. Independent vs dependent events
                        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
                                Regression and Modeling- Linear Relationships
                                • 1. Simple linear regression
                                  • 2. Slope and intercept interpretation

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q42-Q47):

                                    NEW QUESTION # 42
                                    Expected value = ?

                                    Answer: D

                                    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 # 43
                                    Type I error = ?

                                    Answer: C

                                    Explanation:
                                    A Type I error occurs when a statistical test rejects the null hypothesis even though the null hypothesis is actually true. This is often described as a false positive. In practical terms, the test concludes that there is an effect, difference, or relationship when none truly exists under the null condition. The probability of committing a Type I error is denoted by #, the significance level, often set at 0.05. Option B describes a Type II error, where the test fails to reject a false null hypothesis. Option C is not an error at all. Option D is too general; Type I error is not a data-entry issue but a formal decision error in hypothesis testing. The defining phrase is "reject H# when true." Study Guide references/topics: hypothesis testing, Type I error, null hypothesis, significance level.


                                    NEW QUESTION # 44
                                    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 # 45
                                    Standard deviation squared = ?

                                    Answer: C

                                    Explanation:
                                    Variance and standard deviation are directly connected measures of spread. Variance is calculated by averaging squared deviations from the mean, while standard deviation is the square root of variance.
                                    Therefore, reversing that relationship, standard deviation squared equals variance. Symbolically, if the standard deviation is s, then the sample variance is s². This relationship matters because variance is expressed in squared units, while standard deviation is expressed in the original units of measurement. For example, if test-score standard deviation is 4 points, the variance is 4² = 16 square points. The mean and median are measures of center, not squared spread. The standard error measures the variability of a sample statistic, usually the sample mean, across repeated samples. The correct answer is variance because it is the squared form of standard deviation. Study Guide references/topics: standard deviation, variance, measures of spread, descriptive statistics.


                                    NEW QUESTION # 46
                                    Two independent events: P(A and B) = ?

                                    Answer: D

                                    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 # 47
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