Applied-Probability-and-Statistics: Applied Probability and Statistics (FZO1 C955) Dumps & PassGuide Applied-Probability-and-Statistics Examen

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

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

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                                    Applied-Probability-and-Statistics German & Applied-Probability-and-Statistics Prüfungsfragen

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                                    WGU Applied Probability and Statistics (FZO1 C955) Applied-Probability-and-Statistics Prüfungsfragen mit Lösungen (Q108-Q113):

                                    108. Frage
                                    Sample correlation r = 0.6. R² = ?

                                    Antwort: C

                                    Begründung:
                                    The coefficient of determination, R², is obtained by squaring the correlation coefficient r in simple linear regression. Here, r = 0.6, so R² = (0.6)² = 0.36. This means that 36% of the variability in the response variable is explained by the linear relationship with the explanatory variable. The remaining 64% of variability is not explained by that linear model and may be due to other variables, random variation, measurement error, or nonlinear structure. Option B gives the correlation itself, not its square. Option C would come from squaring
                                    0.4, not 0.6. Option D would imply a perfect explanatory relationship, which would require |r| = 1. The value of R² is always between 0 and 1 and is commonly interpreted as a proportion of explained variation. Study Guide references/topics: correlation, coefficient of determination, regression, explained variation.


                                    109. Frage
                                    What is the product of 0.6 and 0.25?

                                    Antwort: B

                                    Begründung:
                                    To multiply decimals, first multiply the numbers as whole numbers and then place the decimal point according to the total number of decimal places in the factors. The values are 0.6 and 0.25. Ignoring decimals temporarily, 6 × 25 = 150. The factor 0.6 has one decimal place, and 0.25 has two decimal places, for a total of three decimal places. Therefore, 150 becomes 0.150, which is equivalent to 0.15. A second way to verify the computation is to convert the decimals into fractions: 0.6 = 6/10 and 0.25 = 25/100. Multiplying gives (6 ×
                                    25)/(10 × 100) = 150/1000 = 0.15. This result is reasonable because one-fourth of 0.6 is 0.15. The other answer choices are too large for one-fourth of 0.6 or do not result from the correct decimal multiplication.
                                    References/topics from the Study Guide: decimal multiplication, fractions, equivalent forms, numerical operations.


                                    110. Frage
                                    A person has a .5 probability of taking a train to work, a .3 probability of carpooling, and a .2 probability of walking. The probability of being late is .2 when taking the train, .1 when carpooling, and .05 when walking.
                                    What is the probability of taking the train and being on time, or walking and being on time?

                                    Antwort: D

                                    Begründung:
                                    This problem combines complements, joint probabilities, and addition of mutually exclusive outcomes. First compute the probability of taking the train and being on time. The probability of being late when taking the train is .2, so the probability of being on time by train is 1 # .2 = .8. Thus, P(train and on time) = .5 × .8 = .40.
                                    Next compute the probability of walking and being on time. The probability of being late when walking is .
                                    05, so the probability of being on time while walking is 1 # .05 = .95. Thus, P(walking and on time) = .2 × .95
                                    = .19. Since a person cannot both take the train and walk as the selected commuting mode, these outcomes are mutually exclusive. Add the two results: .40 + .19 = .59. References/topics from the Study Guide:
                                    complements, conditional probability, joint probability, addition rule.


                                    111. Frage
                                    Empirical probability is based on:

                                    Antwort: D

                                    Begründung:
                                    Empirical probability is based on observed data collected from experiments, surveys, simulations, or repeated trials. It is calculated as the relative frequency of an event: number of times the event occurs divided by the total number of trials or observations. For example, if a machine produces 12 defective items in a sample of
                                    300, the empirical probability of a defect is 12/300 = 0.04. This differs from classical or theoretical probability, which is based on equally likely outcomes and mathematical structure, such as a fair die having probability 1/6 for each face. It also differs from subjective probability, which is based on personal judgment or expert belief rather than observed frequency. The word "empirical" signals evidence obtained through observation, so observed frequency is the correct basis. Study Guide references/topics: empirical probability, relative frequency, observed data, probability interpretation.


                                    112. Frage
                                    Conditional probability formula:

                                    Antwort: B

                                    Begründung:
                                    Conditional probability measures the probability that event A occurs given that event B has already occurred.
                                    The formula is P(A|B) = P(A and B)/P(B), assuming P(B) is greater than zero. The denominator P(B) restricts the sample space to cases where B occurs, and the numerator P(A and B) counts cases where both A and B occur within that restricted space. Option B is incorrect because it divides P(A) by P(B) without requiring overlap between A and B. Option C reverses the conditioning and would relate to P(B|A) only if the numerator were P(A and B). Option D applies to independent events when finding P(A and B), not to conditional probability in general. The vertical bar in P(A|B) is read as "given," and it signals that the denominator should be the probability of the given event. Study Guide references/topics: conditional probability, joint probability, event intersection, probability rules.


                                    113. Frage
                                    ......

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