WGU Applied-Probability-and-Statistics Exam | Applied-Probability-and-Statistics日本語解説集 -権威あるウェブサイトApplied-Probability-and-Statistics学習関連題

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

SectionWeightObjectives
Topic 1: Correlation & Regression20%- Predictions and limitations of regression
- Correlation coefficient and interpretation
- Interpreting slope, intercept, and R-squared
- Simple linear regression models
Topic 2: Basic Numeracy & Algebra15%- Arithmetic operations, fractions, decimals, percentages
- Exponents, roots, and basic formulas
- Linear equations, inequalities, graphing functions
Topic 3: Probability Concepts20%- Probability rules, independent and dependent events
- Discrete and continuous probability distributions
- Normal distribution and empirical rule
- Conditional probability and Venn diagrams
Topic 4: Inferential Statistics & Study Design20%- Confidence intervals for means/proportions
- Sampling methods and bias
- Observational studies vs experiments
- Hypothesis testing framework and interpretation
Topic 5: Descriptive Statistics25%- Measures of spread: range, IQR, variance, standard deviation
- Types of data: categorical, discrete, continuous
- Measures of center: mean, median, mode
- Graphical displays: histograms, boxplots, scatterplots

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WGU Applied Probability and Statistics (FZO1 C955) 認定 Applied-Probability-and-Statistics 試験問題 (Q126-Q131):

質問 # 126
Random variable X = number of heads in 4 coin flips #

正解:A

解説:
The random variable X counts the number of heads obtained in 4 coin flips. Since it is a count, it can take only specific whole-number values: 0, 1, 2, 3, or 4. It cannot take fractional values such as 2.5 heads. A random variable with countable possible outcomes is classified as discrete. This situation also fits a binomial framework because there is a fixed number of independent trials, each trial has two outcomes, and the probability of heads remains constant for a fair coin. A continuous random variable, by contrast, can take any value over an interval, such as time, weight, or height. The number of heads is not measured on a continuum; it is counted. Therefore, the correct classification is discrete. Study Guide references/topics: discrete random variables, binomial setting, coin-flip outcomes, probability distributions.


質問 # 127
The pie chart shows the contribution of different renewable energy sources to the total energy production.

What is true about the given data?

正解:D

解説:
A pie chart displays how a whole is divided into categorical parts, usually as percentages totaling 100%. The chart shows solar at 35%, hydropower at 30%, wind at 20%, geothermal at 10%, and biomass at 5%. The largest percentage is solar, so solar power contributes the most to total energy production. Option A is false because hydropower plus biomass equals 30% + 5% = 35%, which is equal to solar, not more than solar.
Option B is false because geothermal is 10%, while biomass is only 5%; therefore, biomass contributes the least. Option C is false because biomass plus geothermal equals 5% + 10% = 15%, which is less than wind at
20%. The correct interpretation requires comparing category percentages accurately rather than relying on visual size alone. References/topics from the Study Guide: pie charts, categorical data, percentages, interpreting graphical displays.


質問 # 128
Poisson distribution mean = ?

正解:B

解説:
For a Poisson distribution, the mean is #, pronounced "lambda." The parameter # represents the expected number of events occurring in a fixed interval, such as calls per hour, defects per batch, or arrivals per minute.
A defining feature of the Poisson distribution is that both the mean and variance are equal to #. Therefore, if X follows a Poisson distribution with # = 4, then the expected value, or mean, is 4, and the variance is also 4.
Option B and option C are only correct in special cases where # happens to equal 0 or 1, not generally. Option D is conceptually related because the Poisson variance equals #, but the question asks for the mean, and the parameter name is #. The Poisson distribution is used for discrete counts of events over a fixed interval under a constant average rate. Study Guide references/topics: Poisson distribution, expected value, variance, # parameter.


質問 # 129
Correlation coefficient r = #0.9 indicates:

正解:C

解説:
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.


質問 # 130
A city council surveys residents and business owners about a proposed new public transportation system. The results of the survey are shown in the following 2 × 2 contingency table.

Which statement is true?

正解:C

解説:
This question requires comparing conditional percentages from a two-way table. For residents, 150 out of 200 are in favor of the proposed transportation system. The resident support rate is therefore 150/200 = 0.75, or
75%. For business owners, 30 out of 100 are in favor. The business owner support rate is 30/100 = 0.30, or
30%. The difference is 75% # 30% = 45 percentage points, which is a large gap. Therefore, a resident is much more likely than a business owner to favor the new transportation system. Option A understates the magnitude of the difference by calling it slight. Options B and C reverse the direction of the comparison because residents have the higher support rate, not the lower one. The appropriate statistical tool here is conditional percentage because support is being compared within each respondent group. References/topics from the Study Guide: contingency tables, conditional percentages, two-variable categorical data, comparative proportions.


質問 # 131
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