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

SectionObjectives
Topic 1: Descriptive Statistics- Single Variable Data Analysis
  • 1. Measures of dispersion (variance, standard deviation, range)
    • 2. Measures of central tendency (mean, median, mode)
      • 3. Data visualization (histograms, box plots)
        - Two Variable Data Analysis
        • 1. Correlation
          • 2. Outliers and relationships
            • 3. Scatter plots interpretation
              Topic 2: Probability Theory- Probability Distributions
              • 1. Binomial distribution basics
                • 2. Normal distribution
                  - Fundamental Probability Concepts
                  • 1. Basic probability rules
                    • 2. Independent vs dependent events
                      • 3. Conditional probability
                        Topic 3: Regression and Modeling- Linear Relationships
                        • 1. Slope and intercept interpretation
                          • 2. Simple linear regression
                            Topic 4: Statistical Inference- Hypothesis Testing (Introductory Level)
                            • 1. Null vs alternative hypothesis
                              • 2. p-values interpretation
                                - Estimation and Confidence Intervals
                                • 1. Point estimates
                                  • 2. Confidence interval interpretation

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q59-Q64):

                                    NEW QUESTION # 59
                                    Variance formula = ?

                                    Answer: D

                                    Explanation:
                                    The sample variance formula is s² = #(x# # x#)² / (n # 1). In this formula, x# represents each data value, x# is the sample mean, and n is the sample size. The expression x# # x# gives each value's deviation from the mean. Squaring the deviations prevents negative and positive deviations from canceling and emphasizes larger departures. Dividing by n # 1 gives the sample variance, using degrees of freedom to correct bias when estimating population variance from a sample. Option B is the formula for the sample mean, not variance.
                                    Option C squares the mean and does not measure spread. Option D resembles part of the standard deviation process but omits division by n # 1 and is not the variance formula. Variance is foundational because standard deviation is the square root of variance. Study Guide references/topics: variance, sample variance formula, mean deviations, measures of spread.


                                    NEW QUESTION # 60
                                    Variance of Poisson # = 5 = ?

                                    Answer: A

                                    Explanation:
                                    A defining property of the Poisson distribution is that its variance equals its mean, and both are equal to #.
                                    Since the question states # = 5, the variance is also 5. This property distinguishes the Poisson distribution from many other probability distributions. The mean represents the expected number of events per interval, while the variance describes the spread of the event count around that mean. In a Poisson model with # = 5, event counts tend to vary around 5, and the numerical variance is 5. Option B, 4, option C, 0, and option D, 1, do not follow from the Poisson variance rule. The result is not obtained by squaring # or taking its square root; it is simply equal to #. Study Guide references/topics: Poisson distribution, variance, mean, # parameter.


                                    NEW QUESTION # 61
                                    Regression slope indicates:

                                    Answer: C

                                    Explanation:
                                    In a linear regression equation, the slope represents the predicted change in the response variable Y for each one-unit increase in the explanatory variable X. In slope-intercept form, # = b# + b#x, the slope is b#. For example, if a regression equation predicts cost as # = 25 + 4x, the slope 4 means the predicted cost increases by 4 units for each additional unit of x. The intercept, b#, is the predicted value of Y when X = 0, so option B describes a different component. R² measures the proportion of variation in Y explained by the regression model, not the rate of change. Correlation measures strength and direction of linear association, but it is not the same as the slope because it is unitless and standardized. The slope is the operational rate of change in the model. Study Guide references/topics: linear regression, slope interpretation, response variable, explanatory variable.


                                    NEW QUESTION # 62
                                    In a game, a coin is tossed, and a spinner with 8 equal spaces numbered 1 through 8 is spun.
                                    What is the probability of getting heads on the coin and a number less than 3 on the spinner?

                                    Answer: D


                                    NEW QUESTION # 63
                                    There are 10 green, 20 yellow, and 15 purple marbles in a jar.
                                    What is the probability of selecting 2 green marbles in a row and then 1 yellow marble, replacing the marble each time?

                                    Answer: B

                                    Explanation:
                                    There are 10 green, 20 yellow, and 15 purple marbles, so the total number of marbles is 10 + 20 + 15 = 45.
                                    Because each marble is replaced after selection, the probabilities remain the same on every draw, making the events independent. The probability of selecting a green marble on one draw is 10/45 = 2/9. Selecting two green marbles in a row gives (2/9)(2/9). The probability of then selecting a yellow marble is 20/45 = 4/9.
                                    Multiply the probabilities because the question asks for green and green and yellow in that exact sequence: (2
                                    /9)(2/9)(4/9) = 16/729. Replacement is essential; without replacement, the denominators and numerators would change after each draw. Since replacement keeps the sample space constant at 45 marbles each time, the independent multiplication rule applies directly. References/topics from the Study Guide: independent events, replacement, multiplication rule, compound probability.


                                    NEW QUESTION # 64
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