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

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

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q26-Q31):

                                    NEW QUESTION # 26
                                    Standard deviation measures:

                                    Answer: A

                                    Explanation:
                                    Standard deviation measures the spread, variability, or dispersion of data values around the mean. A small standard deviation indicates that the data values are clustered closely around the mean, while a large standard deviation indicates that the values are more widely dispersed. It is calculated from deviations from the mean, squared deviations, variance, and then the square root of variance. Standard deviation is not a measure of central tendency; measures of central tendency include the mean, median, and mode. It is also not a probability, although it is used in probability distributions such as the normal distribution. Frequency refers to how often a value or category occurs, which is summarized with tables, bar charts, histograms, or dot plots.
                                    The standard deviation is essential because it quantifies how consistent or variable a dataset is. Study Guide references/topics: standard deviation, variance, spread, descriptive statistics.


                                    NEW QUESTION # 27
                                    Standard deviation measures:

                                    Answer: B

                                    Explanation:
                                    Standard deviation measures how spread out data values are around the mean. A smaller standard deviation indicates that values are clustered closely near the mean, while a larger standard deviation indicates greater variability. Standard deviation is based on deviations from the mean, squared deviations, variance, and then the square root of variance. It is expressed in the original units of measurement, making it easier to interpret than variance. Option B is incorrect because central tendency is measured by statistics such as the mean, median, and mode. Option C is incorrect because probability measures likelihood, not data dispersion. Option D refers to frequency or the number of observations, not their variability. For example, two classes could have the same mean test score but different standard deviations; the class with the larger standard deviation has more varied scores. Study Guide references/topics: standard deviation, variance, spread, descriptive statistics.


                                    NEW QUESTION # 28
                                    Type I error # = 0.05 means:

                                    Answer: B

                                    Explanation:
                                    The symbol # represents the significance level of a hypothesis test and is the probability of making a Type I error. A Type I error occurs when the null hypothesis is true but the test rejects it. Therefore, # = 0.05 means there is a 5% risk of rejecting a true null hypothesis under the testing procedure. This is often described as the false positive rate. Option B describes a Type II error, which involves failing to reject a false null hypothesis.
                                    Option C is incorrect because a 5% significance level corresponds to a 95% confidence level in related confidence-interval contexts, not 5% confidence. Option D is unrelated; # is not a sample-size percentage.
                                    The interpretation must connect # directly to the probability of incorrectly rejecting H# when H# is actually true. Study Guide references/topics: hypothesis testing, significance level, Type I error, null hypothesis.


                                    NEW QUESTION # 29
                                    Probability of drawing king or queen from deck = ?

                                    Answer: C

                                    Explanation:
                                    A standard deck contains 52 cards. There are 4 kings and 4 queens, one of each rank in each suit. The event is drawing a king or a queen. Since a single card cannot be both a king and a queen, these two events are mutually exclusive. Therefore, the number of favorable outcomes is 4 + 4 = 8. The probability is favorable outcomes divided by total outcomes: 8/52. This fraction can be simplified to 2/13, but the answer choice provides the unsimplified correct form. Option B, 4/52, counts only kings or only queens, not both. Option C,
                                    1/13, is equivalent to 4/52 and again represents one rank only. Option D, 1/26, is too small and does not match the count of favorable cards. The word "or" signals that both qualifying ranks should be included. Study Guide references/topics: card probability, mutually exclusive events, addition rule, sample space.


                                    NEW QUESTION # 30
                                    Uniform distribution 0-10: P(X < 4) = ?

                                    Answer: A

                                    Explanation:
                                    For a continuous uniform distribution from 0 to 10, probability is proportional to interval length because every subinterval of equal length has equal probability density. The total interval length is 10 # 0 = 10. The event X < 4 corresponds to the interval from 0 to 4, which has length 4. Therefore, P(X < 4) = 4/10 = 0.4.
                                    This means 40% of the distribution lies below 4. Option B, 0.6, would correspond to P(X > 4), since the interval from 4 to 10 has length 6. Option C would represent half the interval, such as P(X < 5). Option D does not match the interval proportion. The essential uniform-distribution principle is area equals probability, and with constant density, area reduces to interval length divided by total length. Study Guide references
                                    /topics: uniform distribution, continuous probability, interval length, probability density.


                                    NEW QUESTION # 31
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