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

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

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q107-Q112):

                                    NEW QUESTION # 107
                                    The dot plot illustrates the frequency of outdoor games played by students per week.

                                    Which statement is true?

                                    Answer: C

                                    Explanation:
                                    The dot plot shows a distribution centered near 3 days, with substantial frequencies at 2, 3, and 4 days and smaller frequencies at the extremes of 1 and 5 days. This shape is reasonably balanced around the center.
                                    When a distribution is approximately symmetric, the mean and median tend to be close because the lower and higher values balance each other. The median identifies the middle observation after the data are ordered, and the mean represents the balance point of the distribution. Since the tallest stack is near 3 days and the surrounding stacks on 2 and 4 days are comparable, the center of the data is approximately 3 days by both measures. There is no strong skew to pull the mean far above or below the median. Therefore, the best statement is that the mean is almost the same as the median. Options B and C would require clear skew or extreme imbalance, which the dot plot does not show. References/topics from the Study Guide: dot plots, mean, median, distribution shape, symmetry.


                                    NEW QUESTION # 108
                                    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: A

                                    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 # 109
                                    Two dice rolled, probability of both even = ?

                                    Answer: A

                                    Explanation:
                                    A standard six-sided die has three even outcomes: 2, 4, and 6. Thus, the probability that one die lands on an even number is 3/6 = 1/2. When two dice are rolled, the outcomes are independent because the result of one die does not affect the other. Therefore, the probability that both dice are even is 1/2 × 1/2 = 1/4.
                                    Equivalently, there are 36 ordered outcomes for two dice. The even-even outcomes are formed from 3 even choices on the first die and 3 even choices on the second die, giving 3 × 3 = 9 favorable outcomes. Then 9/36 simplifies to 1/4. Option B gives the probability of one die being even, not both. Options C and D do not match the count or multiplication rule. Study Guide references/topics: independent events, dice probability, multiplication rule, sample space.


                                    NEW QUESTION # 110
                                    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 # 111
                                    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: D

                                    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 # 112
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