WGU Updated Applied-Probability-and-Statistics Exam Questions and Answers by diana

The binomial distribution models the number of successes in a fixed number of independent trials when each trial has only two possible outcomes, usually labeled success and failure, and the probability of success remains constant from trial to trial. These four conditions define the binomial setting: fixed number of trials, independent trials, two outcomes per trial, and constant success probability. Examples include the number of heads in 10 coin flips, the number of defective items in a sample when the defect probability is constant, or the number of students who pass an exam out of a fixed group. The normal distribution describes continuous bell-shaped data, not counts of successes. The Poisson distribution models counts of events occurring over a fixed interval when events occur at a constant average rate. The uniform distribution assigns equal probability across outcomes or intervals. Because the question explicitly states “number of successes” and “fixed independent trials,” the correct model is binomial. Study Guide references/topics: binomial distribution, independent trials, success probability, discrete random variables.

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The question asks for a joint percentage: employees who both prefer working in the office and report high productivity. First identify the percentage who prefer office work. Since 55% prefer remote work, the remaining 45% prefer working in the office. The problem then states that among office-preferring employees, 50% report high productivity. This is a conditional percentage: P(high productivity | office preference) = 50%. To find the overall percentage of all employees who satisfy both conditions, multiply the base percentage by the conditional percentage: 45% × 50% = 0.45 × 0.50 = 0.225 = 22.5%. Option D gives only the conditional rate within the office group, not the percentage of all employees. Option C gives only the office-preference percentage, not productivity within that group. Option B does not match the correct joint probability calculation. The correct selection is therefore 22.5%. References/topics from the Study Guide: probability, conditional percentages, joint probability, two-way categorical reasoning.

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The inequality y ≤ −4x + 1 has boundary line y = −4x + 1. The slope is −4, so the line must decrease steeply from left to right. The y-intercept is 1, so the line must cross the vertical axis at y = 1. Because the inequality uses “≤,” the boundary line must be solid, meaning points on the line are included in the solution set. The solution region must be below the line because y is less than or equal to the expression −4x + 1. A quick test point confirms this. Substitute (0, 0): 0 ≤ −4(0) + 1, giving 0 ≤ 1, which is true. Therefore, the shaded solution region must include the origin. Graph D shows a solid, steep downward-sloping line crossing the y-axis near 1 and shades the region containing the origin and below the boundary. References/topics from the Study Guide: linear inequalities, slope-intercept form, boundary lines, test-point method.

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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.

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