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

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

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q138-Q143):

                                    NEW QUESTION # 138
                                    Standard deviation increases #

                                    Answer: B

                                    Explanation:
                                    Standard deviation measures how far data values typically fall from the mean. When standard deviation increases, the data are more spread out. This means individual observations tend to be farther from the mean, producing greater variability. A smaller standard deviation means the data values are more tightly clustered around the mean. Option B states the opposite of the correct interpretation. Option C is incorrect because an increase in standard deviation does not necessarily mean the mean increases; center and spread are separate features of a distribution. Option D is also incorrect because variance is the square of standard deviation, so if standard deviation increases, variance increases as well, not decreases. Standard deviation is useful because it is expressed in the same units as the original data, making spread easier to interpret. Study Guide references
                                    /topics: standard deviation, variance, spread, measures of variability.


                                    NEW QUESTION # 139
                                    A spinner is divided into four equal sections labeled A, B, C, and D.
                                    What is the sample space for this experiment?

                                    Answer: C

                                    Explanation:
                                    The sample space of a probability experiment is the complete set of all possible outcomes. In this experiment, the spinner has four equal sections labeled A, B, C, and D. Since one spin can land on exactly one of those four labeled sections, the possible outcomes are A, B, C, and D. Therefore, the sample space is {A, B, C, D}.
                                    Option A incorrectly adds E, which is not listed as a section on the spinner. Option B groups labels into combined outcomes, but the experiment is a single spin, not a two-part or paired event. Option C uses numerical labels, but the spinner sections are identified by letters, not numbers. Equal section size affects the probability of each outcome, making each outcome have probability 1/4, but it does not change the sample space itself. References/topics from the Study Guide: probability experiments, outcomes, sample space, equally likely events.


                                    NEW QUESTION # 140
                                    What is the mode of this dataset: 3, 5, 7, 7, 10?

                                    Answer: C

                                    Explanation:
                                    The mode is the value that occurs most frequently in a data set. In the set 3, 5, 7, 7, 10, the value 3 appears once, 5 appears once, 10 appears once, and 7 appears twice. Since 7 has the highest frequency, it is the mode.
                                    This question tests recognition of a measure of center that differs from the mean and median. The mean would require summing all values and dividing by the number of observations, while the median would identify the middle value after ordering the data. The data are already ordered, and the middle value is also 7, but the reason the correct answer is 7 here is specifically because it appears more often than any other value. Options A, B, and D each name values that occur only once, so none can be the mode. A dataset may have one mode, multiple modes, or no mode, but this dataset is unimodal. References/topics from the Study Guide: descriptive statistics, measures of center, frequency, mode.


                                    NEW QUESTION # 141
                                    Null hypothesis for a new drug shows no effect. True statement?

                                    Answer: D

                                    Explanation:
                                    The null hypothesis represents the default claim or baseline assumption in hypothesis testing. For a new drug, a typical null hypothesis states that the drug has no effect, no difference from placebo, or no improvement over the existing standard. The testing process begins by assuming the null hypothesis is true, then evaluates whether the sample evidence is strong enough to reject it. Therefore, the correct statement is that researchers assume no effect until evidence suggests otherwise. This does not mean the drug is proven ineffective; it means the burden of evidence lies with demonstrating an effect. Option B is the alternative hypothesis, not the null. Option C overstates the conclusion because failing to reject the null does not prove the drug has no effect. Option D is false because this type of claim is testable using experimental data and statistical inference.
                                    Study Guide references/topics: null hypothesis, alternative hypothesis, hypothesis testing, statistical evidence.


                                    NEW QUESTION # 142
                                    Expected value = ?

                                    Answer: A

                                    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 # 143
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