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

SectionObjectives
Topic 1: Regression and Modeling- Linear Relationships
  • 1. Slope and intercept interpretation
    • 2. Simple linear regression
      Topic 2: Probability Theory- Fundamental Probability Concepts
      • 1. Conditional probability
        • 2. Independent vs dependent events
          • 3. Basic probability rules
            - Probability Distributions
            • 1. Normal distribution
              • 2. Binomial distribution basics
                Topic 3: Descriptive Statistics- Single Variable Data Analysis
                • 1. Measures of dispersion (variance, standard deviation, range)
                  • 2. Data visualization (histograms, box plots)
                    • 3. Measures of central tendency (mean, median, mode)
                      - Two Variable Data Analysis
                      • 1. Scatter plots interpretation
                        • 2. Correlation
                          • 3. Outliers and relationships
                            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 (Q70-Q75):

                                    NEW QUESTION # 70
                                    Dataset: 3, 5, 7, 9, 11. Median = ?

                                    Answer: A

                                    Explanation:
                                    The median is the center value of an ordered dataset. The values 3, 5, 7, 9, and 11 are already arranged from least to greatest. Because there are five observations, the median is the third value, with two observations below it and two observations above it. The third value is 7, so the median is 7. The median is a measure of central tendency that describes the middle position of the data rather than the arithmetic average. In this dataset, the mean is also 7 because the values are evenly spaced around 7, but the median is determined by position, not by summing and dividing. Option B is the second value, option C is the fourth value, and option D is not a data value. The correct answer is the value that splits the ordered list into two equal halves. Study Guide references/topics: median, ordered data, measures of center, descriptive statistics.


                                    NEW QUESTION # 71
                                    A recording studio raises its use fee to $75 and charges $40 per hour for studio time. The equation of the total cost of a recording session as a function of studio time is y = 40x + 75.
                                    Which graph represents this equation?



                                    Answer: C

                                    Explanation:
                                    The equation y = 40x + 75 is written in slope-intercept form, y = mx + b. In this form, m represents the rate of change and b represents the initial value. The constant term 75 means the graph must cross the y-axis at 75, because the studio charges $75 before any hourly time is added. The coefficient 40 means that for every additional hour of studio time, the total cost increases by $40. Therefore, the correct graph must begin at y =
                                    75 when x = 0 and rise at a steady linear rate of 40 dollars per hour. For example, at x = 6 hours, the model gives y = 40(6) + 75 = 315, so the line should pass near the point (6, 315). Among the displayed graphs, Graph 4 matches both the y-intercept and the slope. References/topics from the Study Guide: basic algebra, linear equations, slope-intercept form, interpreting rate of change.


                                    NEW QUESTION # 72
                                    There are 14 black, 16 white, and 10 red balls in a box.
                                    What is the probability of selecting 1 black ball, then 1 red ball, and then 1 white ball, replacing the ball each time?

                                    Answer: C

                                    Explanation:
                                    The box contains 14 black, 16 white, and 10 red balls, for a total of 40 balls. Because the ball is replaced after each selection, the probability of each color remains constant on every draw. This makes the three draws independent. The probability of selecting a black ball first is 14/40, which simplifies to 7/20. The probability of selecting a red ball second is 10/40, or 1/4. The probability of selecting a white ball third is 16/40, or 2/5.
                                    Since the question asks for all three events in the stated order, multiply the probabilities: (7/20)(1/4)(2/5) = 14
                                    /400 = 7/200. Replacement is the controlling condition; without replacement, the denominators would decrease after each draw. Here, the sample space remains 40 each time. References/topics from the Study Guide: probability, independent events, replacement, multiplication rule.


                                    NEW QUESTION # 73
                                    Standard error decreases when:

                                    Answer: A

                                    Explanation:
                                    The standard error of the sample mean is calculated as SE = s/#n, where s is the sample standard deviation and n is the sample size. Since n appears in the denominator, increasing the sample size reduces the standard error, assuming the standard deviation stays constant. This reflects the fact that larger samples produce more stable estimates of the population mean. Option B is incorrect because decreasing sample size increases standard error. Option C is incorrect because a larger standard deviation increases standard error by increasing the numerator. Option D is incorrect because the mean affects the center of the distribution but does not directly determine the standard error. Standard error is about precision: smaller standard error means less sampling variability and a more precise estimate. That is why larger samples are preferred in inference. Study Guide references/topics: standard error, sample size, standard deviation, sampling variability.


                                    NEW QUESTION # 74
                                    Sample mean = 40, SD = 8, n = 16. Standard error = ?

                                    Answer: C

                                    Explanation:
                                    The standard error of the sample mean is calculated as SE = s/#n, where s is the sample standard deviation and n is the sample size. Here, the standard deviation is 8 and the sample size is 16. The square root of 16 is 4, so SE = 8/4 = 2. The sample mean of 40 is not used directly in the standard error formula; it identifies the center of the sample, not the variability of the sample mean across repeated samples. Option B, 8, is the standard deviation, not the standard error. Option D, 4, is the square root of the sample size. Option C, 0.5, would result from an incorrect calculation. Standard error decreases as sample size increases because larger samples provide more precise estimates. Study Guide references/topics: standard error, standard deviation, sample size, sampling distribution.


                                    NEW QUESTION # 75
                                    ......

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