Excellent Web-Based WGU Applied-Probability-and-Statistics Practice Exam

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

SectionObjectives
Topic 1: Probability Theory- Fundamental Probability Concepts
  • 1. Conditional probability
    • 2. Basic probability rules
      • 3. Independent vs dependent events
        - Probability Distributions
        • 1. Normal distribution
          • 2. Binomial distribution basics
            Topic 2: Regression and Modeling- Linear Relationships
            • 1. Simple linear regression
              • 2. Slope and intercept interpretation
                Topic 3: Statistical Inference- Hypothesis Testing (Introductory Level)
                • 1. Null vs alternative hypothesis
                  • 2. p-values interpretation
                    - Estimation and Confidence Intervals
                    • 1. Confidence interval interpretation
                      • 2. Point estimates
                        Topic 4: 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. Scatter plots interpretation
                                • 2. Outliers and relationships
                                  • 3. Correlation

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q95-Q100):

                                    NEW QUESTION # 95
                                    Central limit theorem states:

                                    Answer: A

                                    Explanation:
                                    The central limit theorem states that, for sufficiently large sample sizes, the sampling distribution of the sample mean is approximately normal, regardless of the shape of the original population distribution, provided observations are independent and drawn appropriately. This is why option A is correct. The theorem does not require the population itself to be normal; if the population is normal, the sample mean is normally distributed for any sample size, but the central limit theorem is especially powerful because it applies broadly for large n. Option C is false because sample variance is an estimate of population variance, not automatically equal to it. Option D is false because standard error generally decreases as sample size increases but does not become exactly zero unless sample size is infinite or variability is absent. The central limit theorem supports confidence intervals and hypothesis tests for means. Study Guide references/topics: central limit theorem, sampling distribution, sample mean, normal approximation.


                                    NEW QUESTION # 96
                                    Probability of rolling an odd number on a die:

                                    Answer: D

                                    Explanation:
                                    A standard six-sided die has six equally likely outcomes: 1, 2, 3, 4, 5, and 6. The odd outcomes are 1, 3, and
                                    5. Thus, there are 3 favorable outcomes out of 6 possible outcomes. The probability is 3/6, which simplifies to
                                    1/2. This means an odd number is just as likely as an even number on a fair die. Option B, 1/3, would represent 2 favorable outcomes out of 6, which is not correct. Option C, 1/6, is the probability of rolling one specific number, such as only a 1. Option D, 2/3, would require 4 favorable outcomes out of 6. Since exactly half the faces are odd, the probability is one-half. Study Guide references/topics: theoretical probability, equally likely outcomes, sample space, favorable outcomes.


                                    NEW QUESTION # 97
                                    Correlation coefficient r = #0.9 indicates:

                                    Answer: B

                                    Explanation:
                                    The correlation coefficient r measures the direction and strength of a linear relationship between two quantitative variables. It ranges from #1 to 1. A value close to #1 indicates a strong negative linear relationship, meaning that as one variable increases, the other tends to decrease in a highly consistent linear pattern. Since r = #0.9 is very close to #1, the relationship is strong and negative. Option B is incorrect because the sign is negative, not positive. Option C identifies the direction correctly but understates the strength; #0.9 is not weak. Option D would correspond to r near 0, where there is little or no linear association. A scatterplot associated with r = #0.9 would show points clustered closely around a downward- sloping line. This does not prove causation; it describes linear association only. Study Guide references
                                    /topics: correlation coefficient, negative association, strength of relationship, scatterplots.


                                    NEW QUESTION # 98
                                    Which distribution models number of successes in fixed independent trials?

                                    Answer: D

                                    Explanation:
                                    The binomial distribution models the number of successes in a fixed number of independent trials when each trial has only two possible outcomes, usually labeled success and failure, and the probability of success remains constant from trial to trial. These four conditions define the binomial setting: fixed number of trials, independent trials, two outcomes per trial, and constant success probability. Examples include the number of heads in 10 coin flips, the number of defective items in a sample when the defect probability is constant, or the number of students who pass an exam out of a fixed group. The normal distribution describes continuous bell-shaped data, not counts of successes. The Poisson distribution models counts of events occurring over a fixed interval when events occur at a constant average rate. The uniform distribution assigns equal probability across outcomes or intervals. Because the question explicitly states "number of successes" and "fixed independent trials," the correct model is binomial. Study Guide references/topics: binomial distribution, independent trials, success probability, discrete random variables.


                                    NEW QUESTION # 99
                                    Probability sum for all outcomes = ?

                                    Answer: A

                                    Explanation:
                                    In any valid probability model, the probabilities of all outcomes in the sample space must sum to 1. The sample space is the complete set of possible outcomes for an experiment, and exactly one outcome from that set must occur. A total probability of 1 represents certainty. For example, when rolling a fair six-sided die, the six outcomes each have probability 1/6, and their sum is 6 × 1/6 = 1. A total of 0 would imply no possible outcome can occur, which is not a valid probability model. A total greater than 1 violates the maximum boundary of probability, and a total less than 1 would mean the sample space is incomplete or some probability has been omitted. This rule is one of the axioms of probability and is used to verify distributions.
                                    Study Guide references/topics: sample space, probability axioms, total probability, probability distributions.


                                    NEW QUESTION # 100
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