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

SectionObjectives
Topic 1: Descriptive Statistics- Data visualization
  • 1. Box plots and interpretation
    • 2. Histograms and frequency distributions
      - Data summarization
      • 1. Measures of variability (range, variance, standard deviation)
        • 2. Measures of central tendency (mean, median, mode)
          Topic 2: 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 3: Statistical Inference- Estimation
                  • 1. Confidence intervals for means and proportions
                    - Hypothesis testing
                    • 1. Null and alternative hypotheses
                      • 2. t-tests and z-tests (basic application)
                        Topic 4: Probability Distributions- Discrete distributions
                        • 1. Poisson distribution (introductory use cases)
                          • 2. Binomial distribution
                            - Continuous distributions
                            • 1. Standard normal and z-scores
                              • 2. Normal distribution
                                Topic 5: Regression and Correlation- Relationship analysis
                                • 1. Simple linear regression basics
                                  • 2. Correlation coefficient interpretation

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                                    Applied-Probability-and-Statistics Exam Practice | Reliable Applied-Probability-and-Statistics Exam Syllabus

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q142-Q147):

                                    NEW QUESTION # 142
                                    Z-score formula = ?

                                    Answer: C

                                    Explanation:
                                    The z-score formula is z = (x # #)/#, where x is the observed value, # is the population mean, and # is the population standard deviation. A z-score standardizes a raw value by measuring how many standard deviations it lies above or below the mean. The numerator, x # #, gives the deviation from the mean. Dividing by # converts that deviation into standard deviation units. If z is positive, the value is above the mean. If z is negative, the value is below the mean. If z = 0, the value equals the mean. Option B incorrectly adds the value and mean, which does not measure deviation. Option C ignores the mean, and option D ignores the observed value entirely. The z-score is central for normal distribution calculations because it allows values from different scales to be compared using the standard normal distribution. Study Guide references/topics: z- scores, standard normal distribution, mean, standard deviation.


                                    NEW QUESTION # 143
                                    Probability it does NOT rain = 1 # 0.25 = ?

                                    Answer: A

                                    Explanation:
                                    This question uses the complement rule of probability. If the probability that it rains is 0.25, then the probability that it does not rain is the complement of that event. The complement rule states that P(not A) = 1
                                    # P(A). Here, A represents the event "it rains," so P(not rain) = 1 # 0.25 = 0.75. This means there is a 75% probability that rain does not occur. Option B repeats the probability of rain rather than its complement.
                                    Option C would imply rain and no rain are equally likely, which is not supported by the given probability.
                                    Option D would mean no rain is certain, but a 0.25 probability of rain means rain is still possible. The key technical point is that an event and its complement must sum to 1. Study Guide references/topics: probability, complement rule, event probability, sample-space total.


                                    NEW QUESTION # 144
                                    Probability it does NOT rain = 1 # 0.25 = ?

                                    Answer: A


                                    NEW QUESTION # 145
                                    Null hypothesis for a new drug shows no effect. True statement?

                                    Answer: C

                                    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 # 146
                                    A tech company surveys its employees to assess remote work preferences. The survey reveals that 55% of employees prefer working remotely, while the remaining employees prefer working in the office. Of the employees who prefer remote work, 75% report high productivity. Among those who prefer working in the office, only 50% report high productivity.
                                    Which percentage of employees prefer working in the office and report high productivity?

                                    Answer: B

                                    Explanation:
                                    The question asks for a joint percentage: employees who both prefer working in the office and report high productivity. First identify the percentage who prefer office work. Since 55% prefer remote work, the remaining 45% prefer working in the office. The problem then states that among office-preferring employees,
                                    50% report high productivity. This is a conditional percentage: P(high productivity | office preference) = 50%.
                                    To find the overall percentage of all employees who satisfy both conditions, multiply the base percentage by the conditional percentage: 45% × 50% = 0.45 × 0.50 = 0.225 = 22.5%. Option D gives only the conditional rate within the office group, not the percentage of all employees. Option C gives only the office-preference percentage, not productivity within that group. Option B does not match the correct joint probability calculation. The correct selection is therefore 22.5%. References/topics from the Study Guide: probability, conditional percentages, joint probability, two-way categorical reasoning.


                                    NEW QUESTION # 147
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