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

SectionObjectives
Topic 1: Probability Distributions- Continuous distributions
  • 1. Normal distribution
    • 2. Standard normal and z-scores
      - Discrete distributions
      • 1. Poisson distribution (introductory use cases)
        • 2. Binomial distribution
          Topic 2: Descriptive Statistics- Data summarization
          • 1. Measures of variability (range, variance, standard deviation)
            • 2. Measures of central tendency (mean, median, mode)
              - Data visualization
              • 1. Box plots and interpretation
                • 2. Histograms and frequency distributions
                  Topic 3: 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)
                          Topic 4: Statistical Inference- Hypothesis testing
                          • 1. Null and alternative hypotheses
                            • 2. t-tests and z-tests (basic application)
                              - Estimation
                              • 1. Confidence intervals for means and proportions
                                Topic 5: Regression and Correlation- Relationship analysis
                                • 1. Correlation coefficient interpretation
                                  • 2. Simple linear regression basics

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                                    Certification Applied-Probability-and-Statistics Training & New Applied-Probability-and-Statistics Mock Exam

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q136-Q141):

                                    NEW QUESTION # 136
                                    A teacher plots the test scores of a class using the box plot.

                                    What is the interquartile range?

                                    Answer: A

                                    Explanation:
                                    The interquartile range, abbreviated IQR, measures the spread of the middle 50% of a data set. In a box plot, the left edge of the box represents the first quartile, Q1, and the right edge of the box represents the third quartile, Q3. The IQR is computed as Q3 # Q1. In the displayed box plot, Q1 is located at 70 points and Q3 is located at approximately 88 points. Therefore, the interquartile range is 88 # 70 = 18 points. The median, shown by the line inside the box, is about 80 points, but the median is not used in the IQR calculation. The whiskers show the approximate minimum and maximum values, but those define the full range, not the interquartile range. The correct answer is 18 points. References/topics from the Study Guide: box plots, quartiles, interquartile range, five-number summary.


                                    NEW QUESTION # 137
                                    Standard deviation measures:

                                    Answer: D

                                    Explanation:
                                    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.


                                    NEW QUESTION # 138
                                    t-test used when:

                                    Answer: A

                                    Explanation:
                                    A t-test is used when making inferences about a population mean and the population standard deviation, #, is unknown. In practical settings, # is rarely available, so the sample standard deviation, s, is used as an estimate.
                                    That substitution introduces additional uncertainty, which is why the t-distribution is used instead of the standard normal distribution. The t-distribution has heavier tails, especially for small samples, reflecting the extra variability caused by estimating # from the sample. Option B describes a z-test setting, where the population standard deviation is known. Option C is incorrect because categorical population data are usually analyzed with proportions, chi-square tests, or related categorical procedures, not mean-based t-tests. Option D is invalid because t-tests have a clear inferential role. The controlling condition is unknown #, with inference focused on means. Study Guide references/topics: t-tests, unknown population standard deviation, sample standard deviation, inferential statistics.


                                    NEW QUESTION # 139
                                    Probability of drawing red card from deck = ?

                                    Answer: B

                                    Explanation:
                                    A standard deck has 52 cards divided into four suits: hearts, diamonds, clubs, and spades. Hearts and diamonds are red, while clubs and spades are black. Each suit has 13 cards, so the number of red cards is 13 +
                                    13 = 26. The probability of drawing a red card is therefore the number of favorable outcomes divided by the total number of outcomes: 26/52. This simplifies to 1/2. Option B, 1/4, would describe the probability of drawing one specific suit, such as hearts only. Option C, 1/13, would describe one specific rank in the deck, such as a particular value across suits. Option D does not correspond to the card structure of a standard deck.
                                    Since exactly half the deck is red, the correct probability is 26/52 = 1/2. Study Guide references/topics: card probability, favorable outcomes, sample space, theoretical probability.


                                    NEW QUESTION # 140
                                    Poisson used for:

                                    Answer: D

                                    Explanation:
                                    The Poisson distribution is used to model counts of events occurring within a fixed interval of time, space, area, or volume, especially when the events are relatively rare and occur at a constant average rate. Examples include the number of calls received per hour, accidents per month, defects per batch, or arrivals at a service counter per minute. Its parameter # represents the average number of events per interval. Option B describes the binomial distribution, which models the number of successes in a fixed number of independent success
                                    /failure trials. Option C is incorrect because Poisson outcomes are discrete counts, not continuous measurements. Option D is also incorrect because categorical data classify observations into groups, while Poisson data count event occurrences. The phrase "rare events per interval" is the defining clue for the Poisson model. Study Guide references/topics: Poisson distribution, rare-event counts, # parameter, discrete probability models.


                                    NEW QUESTION # 141
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