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

SectionObjectives
Topic 1: Probability Distributions- Discrete distributions
  • 1. Poisson distribution (introductory use cases)
    • 2. Binomial distribution
      - Continuous distributions
      • 1. Standard normal and z-scores
        • 2. Normal distribution
          Topic 2: Regression and Correlation- Relationship analysis
          • 1. Simple linear regression basics
            • 2. Correlation coefficient interpretation
              Topic 3: 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 4: Probability- Probability rules
                    • 1. Addition and multiplication rules
                      • 2. Bayes’ theorem (introductory level)
                        - Fundamental probability concepts
                        • 1. Events and sample spaces
                          • 2. Conditional probability and independence
                            Topic 5: Descriptive Statistics- Data visualization
                            • 1. Histograms and frequency distributions
                              • 2. Box plots and interpretation
                                - Data summarization
                                • 1. Measures of variability (range, variance, standard deviation)
                                  • 2. Measures of central tendency (mean, median, mode)

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q43-Q48):

                                    NEW QUESTION # 43
                                    A commuter has a .4 probability of taking the bus to work, a .4 probability of driving a car, and a .2 probability of cycling. The probability of being late is .15 when taking the bus, .05 when driving a car, and .1 when cycling.
                                    What is the probability of taking the bus and being on time, or driving a car and being on time?

                                    Answer: C

                                    Explanation:
                                    This item requires multiplying conditional probabilities and then adding mutually exclusive outcomes.
                                    "Taking the bus and being on time" means the commuter takes the bus and is not late. Since the probability of being late by bus is .15, the probability of being on time by bus is 1 # .15 = .85. Therefore, P(bus and on time)
                                    = .4 × .85 = .34. For driving, the probability of being late is .05, so the probability of being on time is 1 # .05
                                    = .95. Therefore, P(car and on time) = .4 × .95 = .38. Because a commuter cannot both take the bus and drive a car on the same trip, the events are mutually exclusive. Add the two joint probabilities: .34 + .38 = .72. The cycling information is not used because the question asks only about bus-on-time or car-on-time outcomes.
                                    References/topics from the Study Guide: probability rules, complements, conditional probability, mutually exclusive events.


                                    NEW QUESTION # 44
                                    95% CI = 50 ± 2. SE = ?

                                    Answer: C

                                    Explanation:
                                    A confidence interval has the structure estimate ± margin of error. The margin of error is calculated as critical value × standard error. For a 95% confidence interval using the normal approximation, the critical value is approximately 1.96, often rounded to 2 in introductory settings. The interval is given as 50 ± 2, so the margin of error is 2. Using the approximate 95% critical value of 2, we solve 2 = 2 × SE, giving SE = 1. More exactly, using 1.96 gives SE = 2/1.96 # 1.02, which rounds to 1. Option B confuses the margin of error with the standard error. Option C is too large, and option D would produce a margin of error near 1 under a 95% critical value. The correct standard error is approximately 1. Study Guide references/topics: confidence intervals, standard error, critical value, margin of error.


                                    NEW QUESTION # 45
                                    In a normal distribution, 95% of data lies within:

                                    Answer: D

                                    Explanation:
                                    For a normal distribution, the empirical rule states that approximately 68% of data fall within one standard deviation of the mean, approximately 95% fall within two standard deviations, and approximately 99.7% fall within three standard deviations. The notation ±2 SD means two standard deviations below the mean to two standard deviations above the mean, or # # 2# to # + 2#. Therefore, the interval containing about 95% of normally distributed observations is ±2 standard deviations. Option B corresponds to approximately 68%, not
                                    95%. Option C corresponds to approximately 99.7%, and option D extends beyond the standard empirical- rule benchmarks. This concept is central when estimating the typical spread of bell-shaped data, such as test scores, biological measurements, or repeated measurement errors. The correct answer is ±2 SD because it matches the 95% portion of the 68-95-99.7 rule. Study Guide references/topics: normal distribution, empirical rule, standard deviation, distribution spread.


                                    NEW QUESTION # 46
                                    A university surveys faculty and students to determine support for a new campus recycling initiative.
                                    The results of the survey are shown in the following 2 × 2 contingency table:

                                    Which statement is true?

                                    Answer: A

                                    Explanation:
                                    This problem compares conditional percentages across two groups. For faculty members, 40 out of 50 support the recycling initiative, so the faculty support rate is 40/50 = 0.80, or 80%. For students, 200 out of 500 support the initiative, so the student support rate is 200/500 = 0.40, or 40%. Comparing 80% and 40% shows that faculty members are twice as likely as students to support the initiative. This is not a slight difference; it is a large difference of 40 percentage points. Therefore, the correct statement is that faculty members are much more likely than students to support the recycling initiative. The table contains two categorical variables: group type and recycling opinion. Conditional percentages are the appropriate numerical tool because the goal is to compare support within each group. References/topics from the Study Guide:
                                    contingency tables, two-way categorical data, conditional percentages, comparative proportions.


                                    NEW QUESTION # 47
                                    Sum of probabilities in sample space = ?

                                    Answer: C

                                    Explanation:
                                    The probabilities of all outcomes in a complete sample space must sum to 1. A sample space contains every possible outcome of a probability experiment, and one of those outcomes must occur. For example, when rolling a fair six-sided die, the outcomes are 1, 2, 3, 4, 5, and 6. Each has probability 1/6, and the sum is 1/6 +
                                    1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1. A total probability of 0 would mean no outcome can occur, which is impossible for a valid experiment. A total greater than 1 violates probability rules because probabilities cannot exceed certainty. "Cannot exceed 2" is too broad and mathematically invalid, since the exact total must equal
                                    1. This principle is foundational for checking probability distributions and validating whether assigned probabilities are coherent. Study Guide references/topics: sample space, probability axioms, total probability, theoretical probability.


                                    NEW QUESTION # 48
                                    ......

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