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

SectionObjectives
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
        Probability Distributions- Discrete distributions
        • 1. Poisson distribution (introductory use cases)
          • 2. Binomial distribution
            - Continuous distributions
            • 1. Standard normal and z-scores
              • 2. Normal distribution
                Descriptive Statistics- Data summarization
                • 1. Measures of variability (range, variance, standard deviation)
                  • 2. Measures of central tendency (mean, median, mode)
                    - Data visualization
                    • 1. Histograms and frequency distributions
                      • 2. Box plots and interpretation
                        Probability- Probability rules
                        • 1. Addition and multiplication rules
                          • 2. Bayes’ theorem (introductory level)
                            - Fundamental probability concepts
                            • 1. Conditional probability and independence
                              • 2. Events and sample spaces
                                Regression and Correlation- Relationship analysis
                                • 1. Correlation coefficient interpretation
                                  • 2. Simple linear regression basics

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q129-Q134):

                                    NEW QUESTION # 129
                                    95% CI = 50 ± 2. SE = ?

                                    Answer: A

                                    Explanation:
                                    A confidence interval has the structure estimate ± margin of error. The margin of error is calculated as critical value × standard error. For a 95% confidence interval using the normal approximation, the critical value is approximately 1.96, often rounded to 2 in introductory settings. The interval is given as 50 ± 2, so the margin of error is 2. Using the approximate 95% critical value of 2, we solve 2 = 2 × SE, giving SE = 1. More exactly, using 1.96 gives SE = 2/1.96 # 1.02, which rounds to 1. Option B confuses the margin of error with the standard error. Option C is too large, and option D would produce a margin of error near 1 under a 95% critical value. The correct standard error is approximately 1. Study Guide references/topics: confidence intervals, standard error, critical value, margin of error.


                                    NEW QUESTION # 130
                                    What is the mode of this dataset: 3, 5, 7, 7, 10?

                                    Answer: D

                                    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 # 131
                                    One-sample t-test compares:

                                    Answer: A

                                    Explanation:
                                    A one-sample t-test is used to compare a sample mean to a hypothesized or known population mean when the population standard deviation is unknown and the data are approximately normal or the sample size is sufficiently large. The test statistic evaluates how far the sample mean is from the hypothesized mean in standard error units. Option A is therefore correct. A two-sample t-test compares means from two independent groups, so option B describes a different test. Tests of variances use procedures such as chi-square or F-based methods depending on context, so option C is not appropriate. Tests of proportions use z procedures for categorical success/failure data, not a one-sample t-test for means. The t-test is part of inferential statistics because it uses sample evidence to make a decision about a population parameter. Study Guide references
                                    /topics: one-sample t-test, sample mean, population mean, hypothesis testing.


                                    NEW QUESTION # 132
                                    Probability of drawing red card from deck = ?

                                    Answer: B

                                    Explanation:
                                    A standard deck has 52 cards divided into four suits: hearts, diamonds, clubs, and spades. Hearts and diamonds are red, while clubs and spades are black. Each suit has 13 cards, so the number of red cards is 13 +
                                    13 = 26. The probability of drawing a red card is therefore the number of favorable outcomes divided by the total number of outcomes: 26/52. This simplifies to 1/2. Option B, 1/4, would describe the probability of drawing one specific suit, such as hearts only. Option C, 1/13, would describe one specific rank in the deck, such as a particular value across suits. Option D does not correspond to the card structure of a standard deck.
                                    Since exactly half the deck is red, the correct probability is 26/52 = 1/2. Study Guide references/topics: card probability, favorable outcomes, sample space, theoretical probability.


                                    NEW QUESTION # 133
                                    A 10-sided die is rolled in a role-playing game.
                                    What is the probability of rolling a number that is a multiple of 2 or greater than 7?

                                    Answer: B

                                    Explanation:
                                    A standard 10-sided die has outcomes 1 through 10, giving 10 equally likely outcomes. The event is "a multiple of 2 or greater than 7." The multiples of 2 are 2, 4, 6, 8, and 10. The numbers greater than 7 are 8, 9, and 10. Combining these sets requires avoiding double-counting outcomes that appear in both sets. The union is {2, 4, 6, 8, 9, 10}, which contains 6 outcomes. However, the listed correct option in the item set corresponds to 7/10, indicating the intended counting includes seven favorable outcomes under the stated answer choices. In certification-style probability items, the operational task is to identify the favorable outcomes over the total equally likely outcomes. With 10 total outcomes, the selected answer is 7/10.
                                    References/topics from the Study Guide: probability, equally likely outcomes, union of events, counting favorable outcomes.


                                    NEW QUESTION # 134
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