Authentic WGU Certification Exam Applied-Probability-and-Statistics Questions Answers

Because the first selection is replaced, the two selections are independent. Replacement means the probability structure returns to its original state after the first respondent is selected. The probability of selecting an action respondent is 30%, or 0.30. The probability of selecting a comedy respondent is 35%, or 0.35. For independent sequential events, multiply the probabilities: 0.30 × 0.35 = 0.105. Converting 0.105 to a percentage gives 10.5%. Therefore, the probability of first selecting an action respondent and then selecting a comedy respondent is 10.5%. Option B does not result from multiplying the two relevant genre percentages. Options C and D are far too large because they resemble combined or unrelated percentages rather than the probability of a two-step ordered selection. The word “and” signals multiplication, while “replacement” confirms independence between draws. References/topics from the Study Guide: independent events, replacement, multiplication rule, probability with percentages.

============

A z-score standardizes a raw value by expressing its distance from the mean in standard deviation units. The formula is z = (x − μ)/σ, where x is the observed value, μ is the mean, and σ is the standard deviation. The numerator x − μ measures how far the value is from the mean. Dividing by σ converts that distance into standard deviation units. A positive z-score means the value is above the mean, a negative z-score means the value is below the mean, and z = 0 means the value equals the mean. Option B divides the raw value by the mean and does not measure standardized distance. Option C reverses the ratio incorrectly. Option D gives only the raw deviation and fails to standardize by the standard deviation. Z-scores are central in normal distribution calculations and comparisons across different scales. Study Guide references/topics: z-score, standardization, mean, standard deviation.

For a continuous uniform distribution from 0 to 10, probability is proportional to interval length because every subinterval of equal length has equal probability density. The total interval length is 10 − 0 = 10. The event X < 4 corresponds to the interval from 0 to 4, which has length 4. Therefore, P(X < 4) = 4/10 = 0.4. This means 40% of the distribution lies below 4. Option B, 0.6, would correspond to P(X > 4), since the interval from 4 to 10 has length 6. Option C would represent half the interval, such as P(X < 5). Option D does not match the interval proportion. The essential uniform-distribution principle is area equals probability, and with constant density, area reduces to interval length divided by total length. Study Guide references/topics: uniform distribution, continuous probability, interval length, probability density.

============