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

SectionObjectives
Topic 1: Probability- Fundamental probability concepts
  • 1. Events and sample spaces
    • 2. Conditional probability and independence
      - Probability rules
      • 1. Bayes’ theorem (introductory level)
        • 2. Addition and multiplication rules
          Topic 2: Statistical Inference- Hypothesis testing
          • 1. t-tests and z-tests (basic application)
            • 2. Null and alternative hypotheses
              - Estimation
              • 1. Confidence intervals for means and proportions
                Topic 3: 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
                        Topic 4: Probability Distributions- Discrete distributions
                        • 1. Binomial distribution
                          • 2. Poisson distribution (introductory use cases)
                            - 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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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q146-Q151):

                                    NEW QUESTION # 146
                                    Probability it does NOT rain = 1 # 0.25 = ?

                                    Answer: B

                                    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 # 147
                                    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: C

                                    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 # 148
                                    A researcher has collected information on students from a school. The researcher wants to display the ethnic groups represented in the school.
                                    Which pair of graphs both display data in this manner?

                                    Answer: A

                                    Explanation:
                                    Ethnic group is a categorical variable because it classifies students into named groups rather than measuring a numerical quantity. Categorical data are commonly displayed with bar graphs or pie charts. A bar graph shows the frequency or relative frequency of each category using separate bars, making it easy to compare group sizes. A pie chart shows how the whole student population is divided among categories, making it useful for displaying proportions or percentages. Therefore, the correct pair is bar graph and pie chart. A box plot is used for quantitative data and summarizes values using quartiles and a median, so it is not appropriate for ethnic categories. A line graph is typically used to show change over time or ordered numerical trends. A histogram is used for distributions of quantitative data grouped into intervals, not named categories. Since the goal is to display category membership, both selected graphs must support categorical frequency or percentage displays. References/topics from the Study Guide: categorical data displays, bar graphs, pie charts, relative frequency.


                                    NEW QUESTION # 149
                                    Probability of drawing king or queen from deck = ?

                                    Answer: D

                                    Explanation:
                                    A standard deck contains 52 cards. There are 4 kings and 4 queens, one of each rank in each suit. The event is drawing a king or a queen. Since a single card cannot be both a king and a queen, these two events are mutually exclusive. Therefore, the number of favorable outcomes is 4 + 4 = 8. The probability is favorable outcomes divided by total outcomes: 8/52. This fraction can be simplified to 2/13, but the answer choice provides the unsimplified correct form. Option B, 4/52, counts only kings or only queens, not both. Option C,
                                    1/13, is equivalent to 4/52 and again represents one rank only. Option D, 1/26, is too small and does not match the count of favorable cards. The word "or" signals that both qualifying ranks should be included. Study Guide references/topics: card probability, mutually exclusive events, addition rule, sample space.


                                    NEW QUESTION # 150
                                    A sample of 100 houses was surveyed in each of two states: Georgia and Kansas. Square footages of the houses are summarized by state in the following side-by-side box plots.

                                    What is the interquartile range for house sizes in Georgia?

                                    Answer: A

                                    Explanation:
                                    The interquartile range, or IQR, measures the spread of the middle 50% of a distribution. It is calculated as Q3
                                    # Q1, where Q1 is the first quartile and Q3 is the third quartile. In the Georgia box plot, the left edge of the box is labeled 800, representing Q1, and the right edge of the box is labeled 2800, representing Q3. Therefore, the interquartile range is 2800 # 800 = 2000 square feet. The minimum value, 500, and maximum value, 5000, are part of the full range, not the IQR. The median, 1200, identifies the center of the distribution but is not used directly in the IQR calculation. Option D, 4500, corresponds to the full range from 500 to 5000, not the interquartile range. The correct interpretation is that the middle half of Georgia house sizes spans 2000 square feet. References/topics from the Study Guide: box plots, quartiles, interquartile range, comparing distributions.


                                    NEW QUESTION # 151
                                    ......

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