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

SectionWeightObjectives
Topic 1: Inferential Statistics & Study Design20%- Observational studies vs experiments
- Confidence intervals for means/proportions
- Sampling methods and bias
- Hypothesis testing framework and interpretation
Topic 2: Basic Numeracy & Algebra15%- Exponents, roots, and basic formulas
- Arithmetic operations, fractions, decimals, percentages
- Linear equations, inequalities, graphing functions
Topic 3: Correlation & Regression20%- Interpreting slope, intercept, and R-squared
- Correlation coefficient and interpretation
- Predictions and limitations of regression
- Simple linear regression models
Topic 4: Probability Concepts20%- Normal distribution and empirical rule
- Probability rules, independent and dependent events
- Discrete and continuous probability distributions
- Conditional probability and Venn diagrams
Topic 5: Descriptive Statistics25%- Measures of center: mean, median, mode
- Types of data: categorical, discrete, continuous
- Graphical displays: histograms, boxplots, scatterplots
- Measures of spread: range, IQR, variance, standard deviation

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Free PDF 2026 Applied-Probability-and-Statistics: Updated Applied Probability and Statistics (FZO1 C955) Testing Center

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WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q133-Q138):

NEW QUESTION # 133
Sample mean = best point estimate of population mean?

Answer: D

Explanation:
The sample mean is the standard point estimate for the population mean. A point estimate is a single statistic calculated from sample data and used to estimate an unknown population parameter. If the parameter of interest is the population mean #, the corresponding sample statistic is x#. Therefore, the statement is true.
This does not mean the sample mean is guaranteed to equal the population mean exactly; sampling variability can cause sample means to differ from the true population mean. However, the sample mean is unbiased under random sampling and becomes more stable as sample size increases. Confidence intervals expand this idea by placing a margin of error around the sample mean. Option B is incorrect because the sample mean is precisely the conventional point estimator for #. Options C and D impose invalid restrictions. Study Guide references/topics: sample mean, population mean, point estimate, sampling variability.


NEW QUESTION # 134
Standard deviation measures:

Answer: A

Explanation:
Standard deviation measures how spread out data values are around the mean. A smaller standard deviation indicates that values are clustered closely near the mean, while a larger standard deviation indicates greater variability. Standard deviation is based on deviations from the mean, squared deviations, variance, and then the square root of variance. It is expressed in the original units of measurement, making it easier to interpret than variance. Option B is incorrect because central tendency is measured by statistics such as the mean, median, and mode. Option C is incorrect because probability measures likelihood, not data dispersion. Option D refers to frequency or the number of observations, not their variability. For example, two classes could have the same mean test score but different standard deviations; the class with the larger standard deviation has more varied scores. Study Guide references/topics: standard deviation, variance, spread, descriptive statistics.


NEW QUESTION # 135
A t-distribution is used when:

Answer: D

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 # 136
The average lifespan of a dalmatian is 11.5 years, with a standard deviation of 1.5 years.
What are the two values between which 95% of the data falls for the average lifespan of a dalmatian, assuming a normal distribution?

Answer: C

Explanation:
For a normal distribution, the empirical rule states that approximately 95% of observations lie within two standard deviations of the mean. The mean lifespan is 11.5 years, and the standard deviation is 1.5 years. Two standard deviations equal 2 × 1.5 = 3.0 years. Therefore, the interval containing approximately 95% of the data is found by subtracting and adding 3.0 years to the mean: 11.5 # 3.0 = 8.5 and 11.5 + 3.0 = 14.5. The resulting interval is 8.5 years to 14.5 years. Option C, 10.0 to 13.0, represents one standard deviation from the mean and would correspond to about 68% of the data. Options A and D are not centered correctly at the proper two-standard-deviation distance. The correct interval must be symmetric around the mean and use two standard deviations. References/topics from the Study Guide: normal distributions, empirical rule, standard deviation, measures of spread.


NEW QUESTION # 137
Z-score formula = ?

Answer: B

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 # 138
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