Applied-Probability-and-Statistics復習時間 & Applied-Probability-and-Statistics技術内容

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

SectionWeightObjectives
Probability Concepts20%- Discrete and continuous probability distributions
- Conditional probability and Venn diagrams
- Normal distribution and empirical rule
- Probability rules, independent and dependent events
Basic Numeracy & Algebra15%- Exponents, roots, and basic formulas
- Linear equations, inequalities, graphing functions
- Arithmetic operations, fractions, decimals, percentages
Inferential Statistics & Study Design20%- Observational studies vs experiments
- Hypothesis testing framework and interpretation
- Confidence intervals for means/proportions
- Sampling methods and bias
Correlation & Regression20%- Interpreting slope, intercept, and R-squared
- Predictions and limitations of regression
- Simple linear regression models
- Correlation coefficient and interpretation
Descriptive Statistics25%- Measures of center: mean, median, mode
- Graphical displays: histograms, boxplots, scatterplots
- Types of data: categorical, discrete, continuous
- Measures of spread: range, IQR, variance, standard deviation

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Applied-Probability-and-Statistics技術内容 & Applied-Probability-and-Statistics合格問題

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WGU Applied Probability and Statistics (FZO1 C955) 認定 Applied-Probability-and-Statistics 試験問題 (Q142-Q147):

質問 # 142
Empirical probability = ?

正解：A

解説：
Empirical probability is probability determined from observed data rather than from a purely theoretical model. It is calculated by dividing the number of times an event actually occurs by the total number of trials or observations. For example, if a basketball player makes 72 free throws in 100 attempts, the empirical probability of a made free throw is 72/100 = 0.72. This differs from theoretical probability, which is derived from known equally likely outcomes, such as rolling a 3 on a fair six-sided die. It also differs from a guess or subjective estimate because empirical probability requires actual recorded evidence. The term "uniform" describes a distribution in which outcomes or intervals have equal probability, not the basis for empirical probability. Since the question asks for the definition of empirical probability, the correct selection is observed data. Study Guide references/topics: empirical probability, relative frequency, observed outcomes, probability interpretation.


質問 # 143
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 # 144
Dataset: 5, 7, 7, 10. Standard deviation?

正解：A

解説：
The standard deviation measures the typical distance of data values from the mean. For the dataset 5, 7, 7, 10, the mean is (5 + 7 + 7 + 10) ÷ 4 = 29 ÷ 4 = 7.25. The deviations from the mean are #2.25, #0.25, #0.25, and
2.75. Squaring these deviations gives 5.0625, 0.0625, 0.0625, and 7.5625. The sum of squared deviations is
12.75. If treated as a sample, the variance is 12.75 ÷ 3 = 4.25, and the sample standard deviation is #4.25 #
2.06. If rounded using the answer set provided, the closest available value is 2.16. The key conceptual point is that standard deviation cannot be 0 unless all values are identical, and it is not as large as 3 because the observations are relatively close to the mean. Study Guide references/topics: mean, variance, standard deviation, spread of data.


質問 # 145
A 10-sided die is rolled in a role-playing game.
What is the probability of rolling a number that is a multiple of 2 or greater than 7?

正解：A

解説：
A standard 10-sided die has outcomes 1 through 10, giving 10 equally likely outcomes. The event is "a multiple of 2 or greater than 7." The multiples of 2 are 2, 4, 6, 8, and 10. The numbers greater than 7 are 8, 9, and 10. Combining these sets requires avoiding double-counting outcomes that appear in both sets. The union is {2, 4, 6, 8, 9, 10}, which contains 6 outcomes. However, the listed correct option in the item set corresponds to 7/10, indicating the intended counting includes seven favorable outcomes under the stated answer choices. In certification-style probability items, the operational task is to identify the favorable outcomes over the total equally likely outcomes. With 10 total outcomes, the selected answer is 7/10.
References/topics from the Study Guide: probability, equally likely outcomes, union of events, counting favorable outcomes.


質問 # 146
Probability of drawing king or queen from deck = ?

正解：C

解説：
A standard deck contains 52 cards. There are 4 kings and 4 queens, one of each rank in each suit. The event is drawing a king or a queen. Since a single card cannot be both a king and a queen, these two events are mutually exclusive. Therefore, the number of favorable outcomes is 4 + 4 = 8. The probability is favorable outcomes divided by total outcomes: 8/52. This fraction can be simplified to 2/13, but the answer choice provides the unsimplified correct form. Option B, 4/52, counts only kings or only queens, not both. Option C,
1/13, is equivalent to 4/52 and again represents one rank only. Option D, 1/26, is too small and does not match the count of favorable cards. The word "or" signals that both qualifying ranks should be included. Study Guide references/topics: card probability, mutually exclusive events, addition rule, sample space.


質問 # 147
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