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

SectionObjectives
Topic 1: Descriptive Statistics- Data summarization
  • 1. Measures of central tendency (mean, median, mode)
    • 2. Measures of variability (range, variance, standard deviation)
      - Data visualization
      • 1. Box plots and interpretation
        • 2. Histograms and frequency distributions
          Topic 2: 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 3: Regression and Correlation- Relationship analysis
                • 1. Simple linear regression basics
                  • 2. Correlation coefficient interpretation
                    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: Probability Distributions- Discrete distributions
                            • 1. Binomial distribution
                              • 2. Poisson distribution (introductory use cases)
                                - Continuous distributions
                                • 1. Normal distribution
                                  • 2. Standard normal and z-scores

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q66-Q71):

                                    NEW QUESTION # 66
                                    A school surveyed student participation in extracurricular activities. The survey found:
                                    * The drama club had 50% of students participate.
                                    * The science club had 30% of students participate.
                                    * Both clubs had 15% of students participate.
                                    What is the probability that a student participated in the drama club, given that they attended the science club?

                                    Answer: B

                                    Explanation:
                                    This question asks for a conditional probability. The phrase "given that they attended the science club" means the science club group becomes the restricted reference group. The required probability is P(drama club | science club), which is calculated as P(drama and science) divided by P(science). The problem states that 15% of students participated in both clubs, so P(drama and science) = 0.15. It also states that 30% participated in the science club, so P(science) = 0.30. Therefore, P(drama | science) = 0.15 ÷ 0.30 = 0.50. This means that among students who attended the science club, half also participated in drama club. Option A gives the joint probability, not the conditional probability. Option B gives only the science club participation rate. Option C does not match the conditional probability calculation. References/topics from the Study Guide: conditional probability, joint probability, probability ratios, two-event probability.


                                    NEW QUESTION # 67
                                    Standard error decreases when:

                                    Answer: C

                                    Explanation:
                                    The standard error of the mean is calculated as SE = s/#n, where s is the sample standard deviation and n is the sample size. Because n appears in the denominator under a square root, increasing the sample size decreases the standard error when the standard deviation is held constant. This reflects a central idea in sampling: larger samples tend to produce more stable and precise estimates of the population mean. Option C is incorrect because increasing the standard deviation increases the standard error, not decreases it. Option B is incomplete and does not identify what is decreasing. Option D is not the direct driver of standard error; confidence level affects the critical value and margin of error, but the standard error itself is determined by variability and sample size. The correct relationship is inverse: as sample size increases, standard error decreases. Study Guide references/topics: standard error, sample size, sampling variability, precision of estimates.


                                    NEW QUESTION # 68
                                    Determine x:
                                    4 + x = 6 # x

                                    Answer: D

                                    Explanation:
                                    The equation 4 + x = 6 # x is a linear equation in one variable. To solve it, collect variable terms on one side and constant terms on the other. Add x to both sides to eliminate the negative x on the right: 4 + 2x = 6. Then subtract 4 from both sides: 2x = 2. Finally, divide both sides by 2, giving x = 1. This value can be verified directly in the original equation. Substituting x = 1 gives 4 + 1 = 5 on the left and 6 # 1 = 5 on the right, so both sides are equal. Option A gives 4 = 6, which is false. Option C gives 6 = 4, also false. Option D gives 9 =
                                    1, which is not valid. The correct solution is the value that balances both sides of the equation. References
                                    /topics from the Study Guide: basic algebra, solving linear equations, inverse operations, substitution checks.


                                    NEW QUESTION # 69
                                    A standard deck of 52 playing cards, 13 with hearts, 13 with diamonds, 13 with clovers, and 13 with spades, is shuffled, and one card is drawn at random.
                                    What is the probability of drawing a heart?

                                    Answer: C

                                    Explanation:
                                    The probability of a simple event is calculated by dividing the number of favorable outcomes by the total number of equally likely outcomes. A standard deck contains 52 cards. The favorable outcomes are the hearts, and the question states that there are 13 hearts in the deck. Therefore, the probability of drawing a heart is 13
                                    /52. This fraction simplifies by dividing both numerator and denominator by 13, giving 1/4. Option A, 1/13, would incorrectly treat one card as favorable out of 13 rather than 13 favorable hearts out of 52 total cards.
                                    Option B, 1/2, would imply that half the deck consists of hearts, which is false. Option D, 1/3, does not correspond to the four equally sized suits in a standard deck. Since the four suits are equally represented, each suit has probability one out of four. References/topics from the Study Guide: theoretical probability, equally likely outcomes, fractions, sample spaces.


                                    NEW QUESTION # 70
                                    Standard deviation measures:

                                    Answer: C

                                    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 # 71
                                    ......

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