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

SectionObjectives
Topic 1: 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)
          Topic 2: 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 3: Descriptive Statistics- Data summarization
                  • 1. Measures of variability (range, variance, standard deviation)
                    • 2. Measures of central tendency (mean, median, mode)
                      - Data visualization
                      • 1. Box plots and interpretation
                        • 2. Histograms and frequency distributions
                          Topic 4: Statistical Inference- Estimation
                          • 1. Confidence intervals for means and proportions
                            - Hypothesis testing
                            • 1. Null and alternative hypotheses
                              • 2. t-tests and z-tests (basic application)
                                Topic 5: Regression and Correlation- Relationship analysis
                                • 1. Simple linear regression basics
                                  • 2. Correlation coefficient interpretation

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                                    WGU Applied Probability and Statistics (FZO1 C955) 認定 Applied-Probability-and-Statistics 試験問題 (Q18-Q23):

                                    質問 # 18
                                    What percent of data lies within 2 standard deviations of the mean in a normal distribution?

                                    正解：B

                                    解説：
                                    For a normal distribution, the empirical rule, also called the 68-95-99.7 rule, describes how data are distributed around the mean. Approximately 68% of observations fall within 1 standard deviation of the mean, approximately 95% fall within 2 standard deviations, and approximately 99.7% fall within 3 standard deviations. The question asks specifically for the percentage within 2 standard deviations, so the correct value is 95%. This interval is written as # # 2# to # + 2#, where # is the mean and # is the standard deviation.
                                    Option B corresponds to one standard deviation, not two. Option C is an imprecise version of the three- standard-deviation rule, and option D has no standard empirical-rule interpretation in this context. This rule is frequently used to estimate ranges in bell-shaped distributions. Study Guide references/topics: normal distribution, empirical rule, standard deviation, distribution spread.


                                    質問 # 19
                                    Central limit theorem states:

                                    正解：D

                                    解説：
                                    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.


                                    質問 # 20
                                    Binomial distribution parameters = ?

                                    正解：B

                                    解説：
                                    A binomial distribution is defined by two parameters: n and p. The parameter n is the fixed number of trials, and p is the probability of success on each trial. The model applies when trials are independent, each trial has two possible outcomes, and p remains constant. For example, if X is the number of heads in 10 fair coin flips, then X follows a binomial distribution with n = 10 and p = 0.5. Option B, #, is the parameter of a Poisson distribution, used for counts of events over intervals. Option C, # and #, commonly describes a normal distribution, where # is the mean and # is the standard deviation. Option D is incorrect because the binomial model has a precise parameter structure. Identifying n and p is essential before calculating binomial probabilities or expected value. Study Guide references/topics: binomial distribution, independent trials, success probability, discrete probability.


                                    質問 # 21
                                    Probability of rolling an odd number on a die:

                                    正解：C

                                    解説：
                                    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.


                                    質問 # 22
                                    Independent events: P(A|B) = ?

                                    正解：A

                                    解説：
                                    For independent events, the occurrence of one event does not change the probability of the other. Conditional probability P(A|B) means the probability of A occurring given that B has occurred. If A and B are independent, knowing B occurred gives no new information about A. Therefore, P(A|B) = P(A). This is one of the defining properties of independence. For example, if a coin toss and a die roll are independent, knowing the die landed on 4 does not change the probability that the coin landed heads; it remains 1/2. Option B reverses the event being measured. Option C would imply that A becomes impossible after B, which describes a different situation. Option D is an addition expression and does not represent conditional probability. The correct relationship is that the conditional probability equals the original probability when events are independent. Study Guide references/topics: independent events, conditional probability, probability rules, event relationships.


                                    質問 # 23
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