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

The equation y = 40x + 75 is written in slope-intercept form, y = mx + b. In this form, m represents the rate of change and b represents the initial value. The constant term 75 means the graph must cross the y-axis at 75, because the studio charges $75 before any hourly time is added. The coefficient 40 means that for every additional hour of studio time, the total cost increases by $40. Therefore, the correct graph must begin at y = 75 when x = 0 and rise at a steady linear rate of 40 dollars per hour. For example, at x = 6 hours, the model gives y = 40(6) + 75 = 315, so the line should pass near the point (6, 315). Among the displayed graphs, Graph 4 matches both the y-intercept and the slope. References/topics from the Study Guide: basic algebra, linear equations, slope-intercept form, interpreting rate of change.

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This is a binomial probability problem because there is a fixed number of independent trials, each trial has two outcomes, and the probability of success is constant. Let success be flipping heads. There are 3 coin flips, and the probability of heads on each flip is 1/2. The event “exactly two heads” can occur in three ordered ways: HHT, HTH, and THH. Each sequence has probability (1/2)(1/2)(1/2) = 1/8. Since there are three favorable sequences, the total probability is 3 × 1/8 = 3/8. Equivalently, use the binomial formula: C(3,2)(1/2)^2(1/2)^1 = 3 × 1/8 = 3/8. Option B would be too large, and option D counts only one favorable sequence rather than all three. Study Guide references/topics: binomial probability, combinations, independent trials, coin-flip sample spaces.

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The correlation coefficient r measures the direction and strength of a linear relationship between two quantitative variables. Values of r range from −1 to 1. A negative value indicates that as one variable increases, the other variable tends to decrease. The value −0.7 is fairly close to −1, so it represents a strong negative linear relationship. It is not perfect, because perfect negative correlation would be r = −1, but it is clearly stronger than a weak association. Option B is incorrect because the sign is negative, not positive. Option C is incorrect because no linear relationship would be represented by a correlation near 0. Option D is incorrect both in direction and strength. A scatterplot with r = −0.7 would generally show points trending downward from left to right, with some scatter around the trend. Study Guide references/topics: correlation coefficient, negative association, linear relationships, scatterplot interpretation.

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The mode is the value that occurs most frequently in a data set. In the set 3, 5, 7, 7, 10, the value 3 appears once, 5 appears once, 10 appears once, and 7 appears twice. Since 7 has the highest frequency, it is the mode. This question tests recognition of a measure of center that differs from the mean and median. The mean would require summing all values and dividing by the number of observations, while the median would identify the middle value after ordering the data. The data are already ordered, and the middle value is also 7, but the reason the correct answer is 7 here is specifically because it appears more often than any other value. Options A, B, and D each name values that occur only once, so none can be the mode. A dataset may have one mode, multiple modes, or no mode, but this dataset is unimodal. References/topics from the Study Guide: descriptive statistics, measures of center, frequency, mode.