Applied-Probability-and-Statistics科目対策、Applied-Probability-and-Statistics認定資格試験問題集

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

SectionObjectives
Regression and Correlation- Relationship analysis
  • 1. Correlation coefficient interpretation
    • 2. Simple linear regression basics
      Descriptive Statistics- Data visualization
      • 1. Box plots and interpretation
        • 2. Histograms and frequency distributions
          - Data summarization
          • 1. Measures of variability (range, variance, standard deviation)
            • 2. Measures of central tendency (mean, median, mode)
              Statistical Inference- Hypothesis testing
              • 1. Null and alternative hypotheses
                • 2. t-tests and z-tests (basic application)
                  - Estimation
                  • 1. Confidence intervals for means and proportions
                    Probability Distributions- Continuous distributions
                    • 1. Normal distribution
                      • 2. Standard normal and z-scores
                        - Discrete distributions
                        • 1. Binomial distribution
                          • 2. Poisson distribution (introductory use cases)
                            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

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                                    WGU Applied Probability and Statistics (FZO1 C955) 認定 Applied-Probability-and-Statistics 試験問題 (Q97-Q102):

                                    質問 # 97
                                    95% CI = 50 ± 2. SE = ?

                                    正解：D

                                    解説：
                                    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.


                                    質問 # 98
                                    Probability of at least one six in 2 dice rolls = ?

                                    正解：C

                                    解説：
                                    "At least one six" means one six or two sixes across the two rolls. The most efficient method is to use the complement rule. The complement of at least one six is no six on either roll. On one die roll, the probability of not rolling a six is 5/6. Since the two die rolls are independent, the probability of no six on both rolls is (5/6) (5/6) = 25/36. Therefore, the probability of at least one six is 1 # 25/36 = 11/36. This includes all outcomes with a six on the first roll, a six on the second roll, or sixes on both rolls. Option B gives the probability of a six on one single roll only. Option C gives the probability of rolling two sixes. Option D gives the complement, no sixes. Study Guide references/topics: complement rule, independent events, dice probability, sample spaces.


                                    質問 # 99
                                    Z-score formula = ?

                                    正解：A

                                    解説：
                                    The z-score formula is z = (x # #)/#, where x is the observed value, # is the population mean, and # is the population standard deviation. A z-score standardizes a raw value by measuring how many standard deviations it lies above or below the mean. The numerator, x # #, gives the deviation from the mean. Dividing by # converts that deviation into standard deviation units. If z is positive, the value is above the mean. If z is negative, the value is below the mean. If z = 0, the value equals the mean. Option B incorrectly adds the value and mean, which does not measure deviation. Option C ignores the mean, and option D ignores the observed value entirely. The z-score is central for normal distribution calculations because it allows values from different scales to be compared using the standard normal distribution. Study Guide references/topics: z- scores, standard normal distribution, mean, standard deviation.


                                    質問 # 100
                                    A road safety research group wants to enhance road safety by analyzing the stopping distance of a car at different speeds. The group has recorded their data in the following scatterplot.

                                    What is true about the outlier in the scatterplot?

                                    正解：A

                                    解説：
                                    An outlier is a data point that does not follow the general pattern of the remaining data. In this scatterplot, most points show a clear increasing relationship: as speed increases, stopping distance also increases. The main cluster follows a smooth upward trend, with stopping distances gradually rising as speed increases. One point, however, is far above the rest of the pattern. That point is located at approximately 40 mph and 560 feet, making it unusually high compared with the expected stopping distance at that speed. This is why option D correctly identifies the outlier. Option A describes a low-speed point that fits the lower end of the trend.
                                    Option B describes a high-speed point near the upper end of the general pattern, not an unusual deviation.
                                    Option C describes a point around 30 mph and 190 feet, which lies within the main cluster of observations.
                                    The outlier is not merely an extreme x-value or y-value; it is unusual relative to the trend. References/topics from the Study Guide: scatterplots, outliers, bivariate data, association patterns.


                                    質問 # 101
                                    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 # 102
                                    ......

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