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

SectionObjectives
Topic 1: Statistical Inference- Hypothesis testing
  • 1. Null and alternative hypotheses
    • 2. t-tests and z-tests (basic application)
      - Estimation
      • 1. Confidence intervals for means and proportions
        Topic 2: Probability- Fundamental probability concepts
        • 1. Conditional probability and independence
          • 2. Events and sample spaces
            - Probability rules
            • 1. Addition and multiplication rules
              • 2. Bayes’ theorem (introductory level)
                Topic 3: Regression and Correlation- Relationship analysis
                • 1. Simple linear regression basics
                  • 2. Correlation coefficient interpretation
                    Topic 4: Descriptive Statistics- Data summarization
                    • 1. Measures of central tendency (mean, median, mode)
                      • 2. Measures of variability (range, variance, standard deviation)
                        - Data visualization
                        • 1. Histograms and frequency distributions
                          • 2. Box plots and interpretation
                            Topic 5: Probability Distributions- Continuous distributions
                            • 1. Standard normal and z-scores
                              • 2. Normal distribution
                                - Discrete distributions
                                • 1. Poisson distribution (introductory use cases)
                                  • 2. Binomial distribution

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q148-Q153):

                                    NEW QUESTION # 148
                                    Probability cannot be:

                                    Answer: D

                                    Explanation:
                                    Probability values must lie between 0 and 1, inclusive. A probability of 0 means an event is impossible, while a probability of 1 means an event is certain. Values between 0 and 1 represent events with varying degrees of likelihood. A negative probability has no valid interpretation in standard probability theory because probability measures relative likelihood or long-run frequency, and neither can be less than zero. Option B is allowed because impossible events have probability 0. Option C is allowed because certain events have probability 1. Option D is allowed because ordinary uncertain events have probabilities strictly between 0 and
                                    1. For example, the probability of rolling a 3 on a fair die is 1/6, which lies between 0 and 1. The only invalid option listed is negative probability. Study Guide references/topics: probability axioms, probability range, impossible events, certain events.


                                    NEW QUESTION # 149
                                    Uniform distribution 0-5: P(X < 3) = ?

                                    Answer: C

                                    Explanation:
                                    For a continuous uniform distribution on the interval from 0 to 5, probability is proportional to interval length.
                                    The total interval length is 5 # 0 = 5. The event X < 3 corresponds to the interval from 0 to 3, which has length 3. Therefore, P(X < 3) = 3/5 = 0.6. This works because the uniform distribution assigns constant density across the entire interval, so any subinterval's probability equals its length divided by the total length.
                                    Option B would correspond to half the interval, such as X < 2.5. Option C would correspond to length 2 out of
                                    5. Option D incorrectly treats the cutoff value 3 as if it were a percentage rather than an interval boundary.
                                    The correct answer is 0.6, meaning 60% of the uniform distribution lies below 3. Study Guide references
                                    /topics: uniform distribution, continuous probability, interval length, probability density.


                                    NEW QUESTION # 150
                                    Z-test used when:

                                    Answer: B

                                    Explanation:
                                    A z-test for a population mean is used when the population standard deviation # is known and the sampling distribution of the test statistic can be treated as normal. The test statistic has the form z = (sample statistic # hypothesized parameter) divided by the standard error. Knowing # allows the standard error to be computed using #/#n rather than estimating it with the sample standard deviation. Option B describes the common setting for a t-test, not a z-test. Option C is not sufficient by itself; small samples generally require stronger normality assumptions and often favor t-procedures when # is unknown. Option D is unrelated to the classic z- test for a mean, though z-tests can also be used for proportions under appropriate large-sample conditions. In the provided answer set, the defining condition is that the population standard deviation is known. Study Guide references/topics: z-test, population standard deviation, standard error, hypothesis testing.


                                    NEW QUESTION # 151
                                    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: D

                                    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 # 152
                                    A dataset: 4, 8, 12, 16, 20. Mean = ?

                                    Answer: C

                                    Explanation:
                                    The mean is the arithmetic average of a data set. To compute it, add all values and divide by the number of observations. For the dataset 4, 8, 12, 16, and 20, the sum is 4 + 8 + 12 + 16 + 20 = 60. There are 5 values, so the mean is 60 ÷ 5 = 12. The mean represents the balance point of the data. This dataset is evenly spaced around 12: 4 and 20 are equally distant from 12, and 8 and 16 are equally distant from 12. That symmetry supports the computed result. Option A, 10, is too low because it does not account for the higher values 16 and 20. Option C, 14, is too high, and option D is one of the data values but not the average. The correct answer is 12. Study Guide references/topics: mean, arithmetic average, measures of center, quantitative data.


                                    NEW QUESTION # 153
                                    ......

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