Applied-Probability-and-Statistics Certification Exam Infor | Applied-Probability-and-Statistics Reliable Exam Questions

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

SectionObjectives
Topic 1: Probability- Fundamental probability concepts
  • 1. Events and sample spaces
    • 2. Conditional probability and independence
      - Probability rules
      • 1. Bayes’ theorem (introductory level)
        • 2. Addition and multiplication rules
          Topic 2: Regression and Correlation- Relationship analysis
          • 1. Correlation coefficient interpretation
            • 2. Simple linear regression basics
              Topic 3: Descriptive Statistics- Data summarization
              • 1. Measures of central tendency (mean, median, mode)
                • 2. Measures of variability (range, variance, standard deviation)
                  - Data visualization
                  • 1. Histograms and frequency distributions
                    • 2. Box plots and interpretation
                      Topic 4: Statistical Inference- Estimation
                      • 1. Confidence intervals for means and proportions
                        - Hypothesis testing
                        • 1. Null and alternative hypotheses
                          • 2. t-tests and z-tests (basic application)
                            Topic 5: Probability Distributions- Continuous distributions
                            • 1. Normal distribution
                              • 2. Standard normal and z-scores
                                - Discrete distributions
                                • 1. Poisson distribution (introductory use cases)
                                  • 2. Binomial distribution

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q62-Q67):

                                    NEW QUESTION # 62
                                    Independent events: P(A|B) = ?

                                    Answer: B

                                    Explanation:
                                    For independent events, the occurrence of one event does not change the probability of the other. Conditional probability P(A|B) means the probability of A occurring given that B has occurred. If A and B are independent, knowing B occurred gives no new information about A. Therefore, P(A|B) = P(A). This is one of the defining properties of independence. For example, if a coin toss and a die roll are independent, knowing the die landed on 4 does not change the probability that the coin landed heads; it remains 1/2. Option B reverses the event being measured. Option C would imply that A becomes impossible after B, which describes a different situation. Option D is an addition expression and does not represent conditional probability. The correct relationship is that the conditional probability equals the original probability when events are independent. Study Guide references/topics: independent events, conditional probability, probability rules, event relationships.


                                    NEW QUESTION # 63
                                    Probability cannot be:

                                    Answer: A

                                    Explanation:
                                    Probability values must lie between 0 and 1, inclusive. A probability of 0 means an event is impossible, while a probability of 1 means an event is certain. Values between 0 and 1 represent events with varying degrees of likelihood. A negative probability has no valid interpretation in standard probability theory because probability measures relative likelihood or long-run frequency, and neither can be less than zero. Option B is allowed because impossible events have probability 0. Option C is allowed because certain events have probability 1. Option D is allowed because ordinary uncertain events have probabilities strictly between 0 and
                                    1. For example, the probability of rolling a 3 on a fair die is 1/6, which lies between 0 and 1. The only invalid option listed is negative probability. Study Guide references/topics: probability axioms, probability range, impossible events, certain events.


                                    NEW QUESTION # 64
                                    Standard error decreases when:

                                    Answer: C

                                    Explanation:
                                    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.


                                    NEW QUESTION # 65
                                    Determine z in the equation:
                                    1/(6z) = 2/9

                                    Answer: B

                                    Explanation:
                                    The equation 1/(6z) = 2/9 is a proportion because it sets two fractions equal to each other. To solve it, use cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction, and multiply the denominator of the first fraction by the numerator of the second fraction: 1 × 9 = 2 × 6z. This gives 9 = 12z. To isolate z, divide both sides by 12: z = 9/12. This fraction can also be simplified to 3/4, but the answer choices list the unsimplified equivalent form 9/12. The other options do not satisfy the original equation. For example, if z = 2/54, then 6z is very small and the left side becomes much larger than 2/9. If z =
                                    12/9 or 18/2, the denominator becomes too large, making the left side too small. References/topics from the Study Guide: proportions, solving equations, cross multiplication, equivalent fractions.


                                    NEW QUESTION # 66
                                    Z-score formula = ?

                                    Answer: D

                                    Explanation:
                                    The z-score formula is z = (x # #)/#, where x is the observed value, # is the population mean, and # is the population standard deviation. A z-score standardizes a raw value by measuring how many standard deviations it lies above or below the mean. The numerator, x # #, gives the deviation from the mean. Dividing by # converts that deviation into standard deviation units. If z is positive, the value is above the mean. If z is negative, the value is below the mean. If z = 0, the value equals the mean. Option B incorrectly adds the value and mean, which does not measure deviation. Option C ignores the mean, and option D ignores the observed value entirely. The z-score is central for normal distribution calculations because it allows values from different scales to be compared using the standard normal distribution. Study Guide references/topics: z- scores, standard normal distribution, mean, standard deviation.


                                    NEW QUESTION # 67
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