Applied-Probability-and-Statistics Studienmaterialien: Applied Probability and Statistics (FZO1 C955) - Applied-Probability-and-Statistics Torrent Prüfung & Applied-Probability-and-Statistics wirkliche Prüfung

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

SectionObjectives
Probability Distributions- Continuous distributions
  • 1. Normal distribution
    • 2. Standard normal and z-scores
      - Discrete distributions
      • 1. Poisson distribution (introductory use cases)
        • 2. Binomial distribution
          Probability- Probability rules
          • 1. Bayes’ theorem (introductory level)
            • 2. Addition and multiplication rules
              - Fundamental probability concepts
              • 1. Events and sample spaces
                • 2. Conditional probability and independence
                  Statistical Inference- Estimation
                  • 1. Confidence intervals for means and proportions
                    - Hypothesis testing
                    • 1. t-tests and z-tests (basic application)
                      • 2. Null and alternative hypotheses
                        Descriptive Statistics- Data summarization
                        • 1. Measures of central tendency (mean, median, mode)
                          • 2. Measures of variability (range, variance, standard deviation)
                            - Data visualization
                            • 1. Box plots and interpretation
                              • 2. Histograms and frequency distributions
                                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) Applied-Probability-and-Statistics Prüfungsfragen mit Lösungen (Q121-Q126):

                                    121. Frage
                                    A university surveys faculty and students to determine support for a new campus recycling initiative.
                                    The results of the survey are shown in the following 2 × 2 contingency table:

                                    Which statement is true?

                                    Antwort: C

                                    Begründung:
                                    This problem compares conditional percentages across two groups. For faculty members, 40 out of 50 support the recycling initiative, so the faculty support rate is 40/50 = 0.80, or 80%. For students, 200 out of 500 support the initiative, so the student support rate is 200/500 = 0.40, or 40%. Comparing 80% and 40% shows that faculty members are twice as likely as students to support the initiative. This is not a slight difference; it is a large difference of 40 percentage points. Therefore, the correct statement is that faculty members are much more likely than students to support the recycling initiative. The table contains two categorical variables: group type and recycling opinion. Conditional percentages are the appropriate numerical tool because the goal is to compare support within each group. References/topics from the Study Guide:
                                    contingency tables, two-way categorical data, conditional percentages, comparative proportions.


                                    122. Frage
                                    Standard deviation measures:

                                    Antwort: C

                                    Begründung:
                                    Standard deviation measures the spread, variability, or dispersion of data values around the mean. A small standard deviation indicates that the data values are clustered closely around the mean, while a large standard deviation indicates that the values are more widely dispersed. It is calculated from deviations from the mean, squared deviations, variance, and then the square root of variance. Standard deviation is not a measure of central tendency; measures of central tendency include the mean, median, and mode. It is also not a probability, although it is used in probability distributions such as the normal distribution. Frequency refers to how often a value or category occurs, which is summarized with tables, bar charts, histograms, or dot plots.
                                    The standard deviation is essential because it quantifies how consistent or variable a dataset is. Study Guide references/topics: standard deviation, variance, spread, descriptive statistics.


                                    123. Frage
                                    One-sample t-test compares:

                                    Antwort: C

                                    Begründung:
                                    A one-sample t-test is used to compare a sample mean to a hypothesized or known population mean when the population standard deviation is unknown and the data are approximately normal or the sample size is sufficiently large. The test statistic evaluates how far the sample mean is from the hypothesized mean in standard error units. Option A is therefore correct. A two-sample t-test compares means from two independent groups, so option B describes a different test. Tests of variances use procedures such as chi-square or F-based methods depending on context, so option C is not appropriate. Tests of proportions use z procedures for categorical success/failure data, not a one-sample t-test for means. The t-test is part of inferential statistics because it uses sample evidence to make a decision about a population parameter. Study Guide references
                                    /topics: one-sample t-test, sample mean, population mean, hypothesis testing.


                                    124. Frage
                                    Standard error decreases when:

                                    Antwort: C

                                    Begründung:
                                    The standard error of the sample mean is calculated as SE = s/#n, where s is the sample standard deviation and n is the sample size. Since n appears in the denominator, increasing the sample size reduces the standard error, assuming the standard deviation stays constant. This reflects the fact that larger samples produce more stable estimates of the population mean. Option B is incorrect because decreasing sample size increases standard error. Option C is incorrect because a larger standard deviation increases standard error by increasing the numerator. Option D is incorrect because the mean affects the center of the distribution but does not directly determine the standard error. Standard error is about precision: smaller standard error means less sampling variability and a more precise estimate. That is why larger samples are preferred in inference. Study Guide references/topics: standard error, sample size, standard deviation, sampling variability.


                                    125. Frage
                                    Central limit theorem applies when:

                                    Antwort: B

                                    Begründung:
                                    The central limit theorem applies when the sample size is sufficiently large and observations are independent.
                                    It states that the sampling distribution of the sample mean becomes approximately normal as sample size increases, even if the original population distribution is not normal. This makes option A correct. Option B is incorrect because the population does not have to be normal for the theorem to operate; large sample size is what permits the normal approximation. Option C is not the condition that defines the theorem. A population parameter may be unknown in inference, but that is not the trigger for the central limit theorem. Option D is incorrect because the classic central limit theorem for means concerns quantitative data, not purely categorical labels. The theorem is foundational because it justifies using normal-based confidence intervals and hypothesis tests for means when sample sizes are large. Study Guide references/topics: central limit theorem, sample size, sampling distribution, normal approximation.


                                    126. Frage
                                    ......

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