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

SectionObjectives
Topic 1: Probability- Fundamental probability concepts
  • 1. Conditional probability and independence
    • 2. Events and sample spaces
      - Probability rules
      • 1. Bayes’ theorem (introductory level)
        • 2. Addition and multiplication rules
          Topic 2: 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
                Topic 3: Regression and Correlation- Relationship analysis
                • 1. Correlation coefficient interpretation
                  • 2. Simple linear regression basics
                    Topic 4: Probability Distributions- Continuous distributions
                    • 1. Standard normal and z-scores
                      • 2. Normal distribution
                        - Discrete distributions
                        • 1. Binomial distribution
                          • 2. Poisson distribution (introductory use cases)
                            Topic 5: 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)

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                                    100% Pass 2026 WGU High Hit-Rate Applied-Probability-and-Statistics: Dumps Applied Probability and Statistics (FZO1 C955) Vce

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q68-Q73):

                                    NEW QUESTION # 68
                                    In a game, a coin is tossed, and a spinner with 8 equal spaces numbered 1 through 8 is spun.
                                    What is the probability of getting heads on the coin and a number less than 3 on the spinner?

                                    Answer: D


                                    NEW QUESTION # 69
                                    Central limit theorem applies when:

                                    Answer: C

                                    Explanation:
                                    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.


                                    NEW QUESTION # 70
                                    A child's parents want to analyze the relationship between the daily high temperature and ice cream sales at their child's ice cream stand. They create the following scatterplot.

                                    What is the estimated value of r, the correlation coefficient, between these variables?

                                    Answer: B

                                    Explanation:
                                    The correlation coefficient r measures both the direction and strength of a linear relationship between two quantitative variables. In this scatterplot, the points rise from lower left to upper right, showing a positive association between temperature and daily ice cream sales. As temperature increases, sales also tend to increase. The points are fairly close to an upward-sloping linear pattern, so the relationship is strong rather than weak. A value of r near 1 indicates a strong positive linear association, while a value near #1 indicates a strong negative association. Since the association is clearly positive, the negative options, #0.93 and #0.39, are not appropriate. Since the points show a strong trend rather than a loose or weak trend, 0.39 is too small.
                                    The best estimate is 0.93. This is consistent with the visual pattern: temperature explains a substantial amount of the linear movement in ice cream sales. References/topics from the Study Guide: scatterplots, correlation coefficient, positive association, strength of linear relationship.


                                    NEW QUESTION # 71
                                    Probability it does NOT rain = 1 # 0.25 = ?

                                    Answer: B

                                    Explanation:
                                    This question uses the complement rule of probability. If the probability that it rains is 0.25, then the probability that it does not rain is the complement of that event. The complement rule states that P(not A) = 1
                                    # P(A). Here, A represents the event "it rains," so P(not rain) = 1 # 0.25 = 0.75. This means there is a 75% probability that rain does not occur. Option B repeats the probability of rain rather than its complement.
                                    Option C would imply rain and no rain are equally likely, which is not supported by the given probability.
                                    Option D would mean no rain is certain, but a 0.25 probability of rain means rain is still possible. The key technical point is that an event and its complement must sum to 1. Study Guide references/topics: probability, complement rule, event probability, sample-space total.


                                    NEW QUESTION # 72
                                    A gardener records the length of a plant over a duration of 35 weeks. The scatterplot shows the data.

                                    What is the relationship between length and time?

                                    Answer: A

                                    Explanation:
                                    The scatterplot shows time on the horizontal axis and plant length on the vertical axis. As time increases, the plotted plant lengths also increase. This upward pattern indicates a positive relationship. The points are not randomly scattered; they follow a clear rising trend from approximately 3 inches at the beginning to more than 9 inches near the end of the observation period. Because the points cluster closely around an increasing pattern, the relationship is strong rather than weak. A negative relationship would require plant length to decrease as time increases, which is not shown. A weak positive relationship would show only a slight upward tendency with substantial scatter, but this graph shows a consistent increase across the weeks.
                                    Therefore, the best description is a strong positive relationship between time and plant height or length.
                                    References/topics from the Study Guide: scatterplots, association, positive correlation, strength of relationship.


                                    NEW QUESTION # 73
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