Valid WGU Applied-Probability-and-Statistics Test Question - Questions Applied-Probability-and-Statistics Pdf

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

SectionObjectives
Descriptive Statistics- Single Variable Data Analysis
  • 1. Data visualization (histograms, box plots)
    • 2. Measures of central tendency (mean, median, mode)
      • 3. Measures of dispersion (variance, standard deviation, range)
        - Two Variable Data Analysis
        • 1. Scatter plots interpretation
          • 2. Correlation
            • 3. Outliers and relationships
              Regression and Modeling- Linear Relationships
              • 1. Slope and intercept interpretation
                • 2. Simple linear regression
                  Statistical Inference- Estimation and Confidence Intervals
                  • 1. Confidence interval interpretation
                    • 2. Point estimates
                      - Hypothesis Testing (Introductory Level)
                      • 1. Null vs alternative hypothesis
                        • 2. p-values interpretation
                          Probability Theory- Probability Distributions
                          • 1. Normal distribution
                            • 2. Binomial distribution basics
                              - Fundamental Probability Concepts
                              • 1. Independent vs dependent events
                                • 2. Conditional probability
                                  • 3. Basic probability rules

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q80-Q85):

                                    NEW QUESTION # 80
                                    There are 14 black, 16 white, and 10 red balls in a box.
                                    What is the probability of selecting 1 black ball, then 1 red ball, and then 1 white ball, replacing the ball each time?

                                    Answer: C

                                    Explanation:
                                    The box contains 14 black, 16 white, and 10 red balls, for a total of 40 balls. Because the ball is replaced after each selection, the probability of each color remains constant on every draw. This makes the three draws independent. The probability of selecting a black ball first is 14/40, which simplifies to 7/20. The probability of selecting a red ball second is 10/40, or 1/4. The probability of selecting a white ball third is 16/40, or 2/5.
                                    Since the question asks for all three events in the stated order, multiply the probabilities: (7/20)(1/4)(2/5) = 14
                                    /400 = 7/200. Replacement is the controlling condition; without replacement, the denominators would decrease after each draw. Here, the sample space remains 40 each time. References/topics from the Study Guide: probability, independent events, replacement, multiplication rule.


                                    NEW QUESTION # 81
                                    A sample of 100 houses was surveyed in each of two states: Georgia and Kansas. Square footages of the houses are summarized by state in the following side-by-side box plots.

                                    What is the interquartile range for house sizes in Georgia?

                                    Answer: A

                                    Explanation:
                                    The interquartile range, or IQR, measures the spread of the middle 50% of a distribution. It is calculated as Q3
                                    # Q1, where Q1 is the first quartile and Q3 is the third quartile. In the Georgia box plot, the left edge of the box is labeled 800, representing Q1, and the right edge of the box is labeled 2800, representing Q3. Therefore, the interquartile range is 2800 # 800 = 2000 square feet. The minimum value, 500, and maximum value, 5000, are part of the full range, not the IQR. The median, 1200, identifies the center of the distribution but is not used directly in the IQR calculation. Option D, 4500, corresponds to the full range from 500 to 5000, not the interquartile range. The correct interpretation is that the middle half of Georgia house sizes spans 2000 square feet. References/topics from the Study Guide: box plots, quartiles, interquartile range, comparing distributions.


                                    NEW QUESTION # 82
                                    A t-distribution is used when:

                                    Answer: C

                                    Explanation:
                                    A t-distribution is used for inference about a population mean when the population standard deviation # is unknown, especially with a small sample. In that situation, the sample standard deviation s must estimate #, creating extra uncertainty. The t-distribution accounts for this added uncertainty with heavier tails than the standard normal distribution. As sample size increases, the t-distribution becomes closer to the normal distribution. Option B describes a z-procedure setting, where # is known and the normal distribution may be used. Option C is incorrect because categorical data are usually analyzed with proportions or chi-square procedures, not t-distributions for means. Option D is incomplete: t-procedures typically require quantitative continuous or approximately continuous data, but the decisive condition in the answer set is unknown # with a small sample. Study Guide references/topics: t-distribution, unknown standard deviation, small samples, inference for means.


                                    NEW QUESTION # 83
                                    Probability of rolling an even number on a six-sided die?

                                    Answer: A

                                    Explanation:
                                    A standard six-sided die has six equally likely outcomes: 1, 2, 3, 4, 5, and 6. The even outcomes are 2, 4, and
                                    6. That gives 3 favorable outcomes out of 6 total outcomes. Therefore, the probability of rolling an even number is 3/6, which simplifies to 1/2. Option A, 1/3, would correspond to 2 favorable outcomes out of 6, which is not correct here. Option C, 1/6, is the probability of rolling one specific number, such as only a 2.
                                    Option D, 2/3, would require 4 favorable outcomes out of 6. Since exactly half of the die faces are even and half are odd, the probability of rolling an even number is one-half. Study Guide references/topics: theoretical probability, equally likely outcomes, sample space, favorable outcomes.


                                    NEW QUESTION # 84
                                    In a class of 40 students, the following data were collected on their favorite sport:
                                    * Soccer: 10 students
                                    * Basketball: 15 students
                                    * Tennis: 5 students
                                    * Swimming: 10 students
                                    What is the relative frequency of students whose favorite sport is not basketball?

                                    Answer: C

                                    Explanation:
                                    Relative frequency is the proportion of observations in a category compared with the total number of observations. The class has 40 students. Basketball accounts for 15 students, so the number of students whose favorite sport is not basketball is 40 # 15 = 25. The relative frequency is therefore 25/40. Dividing gives
                                    0.625. This means 62.5% of the class selected a sport other than basketball. The same result can be found by adding the non-basketball categories directly: soccer 10, tennis 5, and swimming 10, giving 10 + 5 + 10 = 25 students. Option A, 0.25, corresponds to 10 out of 40 and would represent soccer or swimming alone. Option B, 0.50, corresponds to 20 out of 40. Option D, 0.75, would imply 30 students, which is too high. References
                                    /topics from the Study Guide: relative frequency, categorical data, frequency tables, proportions.


                                    NEW QUESTION # 85
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