Pass the WGU Courses and Certificates Applied-Probability-and-Statistics Questions and answers with CertsForce

To add and subtract fractions, first rewrite all fractions using a common denominator. The denominators are 5, 3, and 4. Their least common denominator is 60. Convert each fraction: 2/5 = 24/60, 1/3 = 20/60, and 1/4 = 15/60. Now combine the numerators while keeping the common denominator: 24/60 + 20/60 − 15/60 = (24 + 20 − 15)/60 = 29/60. The fraction 29/60 is already in simplest form because 29 is prime and does not divide 60. Option A, 13/60, and option B, 11/60, result from incorrect numerator operations. Option D, 19/60, also fails to preserve the correct addition before subtraction. The essential technical step is establishing a common denominator before performing arithmetic operations. References/topics from the Study Guide: fractions, least common denominator, fraction addition, fraction subtraction.

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The dot plot shows a distribution centered near 3 days, with substantial frequencies at 2, 3, and 4 days and smaller frequencies at the extremes of 1 and 5 days. This shape is reasonably balanced around the center. When a distribution is approximately symmetric, the mean and median tend to be close because the lower and higher values balance each other. The median identifies the middle observation after the data are ordered, and the mean represents the balance point of the distribution. Since the tallest stack is near 3 days and the surrounding stacks on 2 and 4 days are comparable, the center of the data is approximately 3 days by both measures. There is no strong skew to pull the mean far above or below the median. Therefore, the best statement is that the mean is almost the same as the median. Options B and C would require clear skew or extreme imbalance, which the dot plot does not show. References/topics from the Study Guide: dot plots, mean, median, distribution shape, symmetry.

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A defining property of the Poisson distribution is that its variance equals its mean, and both are equal to λ. Since the question states λ = 5, the variance is also 5. This property distinguishes the Poisson distribution from many other probability distributions. The mean represents the expected number of events per interval, while the variance describes the spread of the event count around that mean. In a Poisson model with λ = 5, event counts tend to vary around 5, and the numerical variance is 5. Option B, 4, option C, 0, and option D, 1, do not follow from the Poisson variance rule. The result is not obtained by squaring λ or taking its square root; it is simply equal to λ. Study Guide references/topics: Poisson distribution, variance, mean, λ parameter.

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The standard error of the mean measures the expected sampling variability of the sample mean. It is calculated by dividing the sample standard deviation by the square root of the sample size: SE = s / √n. In this question, the standard deviation is 5 and the sample size is 25. Therefore, SE = 5 / √25 = 5 / 5 = 1. The mean of 50 identifies the center of the sample distribution but is not directly used in the standard error calculation. Option B, 5, is the standard deviation, not the standard error. Option C, 25, is the sample size. Option D, 0.2, would result from incorrectly dividing 5 by 25 rather than by the square root of 25. The distinction between standard deviation and standard error is important: standard deviation describes spread among individual observations, while standard error describes spread among sample means. Study Guide references/topics: standard error, standard deviation, sample size, sampling distributions.

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For a continuous uniform distribution on the interval from 0 to 5, probability is proportional to interval length. The total interval length is 5 − 0 = 5. The event X < 3 corresponds to the interval from 0 to 3, which has length 3. Therefore, P(X < 3) = 3/5 = 0.6. This works because the uniform distribution assigns constant density across the entire interval, so any subinterval’s probability equals its length divided by the total length. Option B would correspond to half the interval, such as X < 2.5. Option C would correspond to length 2 out of 5. Option D incorrectly treats the cutoff value 3 as if it were a percentage rather than an interval boundary. The correct answer is 0.6, meaning 60% of the uniform distribution lies below 3. Study Guide references/topics: uniform distribution, continuous probability, interval length, probability density.

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The median is the middle value of a data set after the values are placed in ascending order. The dataset is 3, 6, 9, which is already ordered from least to greatest. Since there are three observations, the median is the second value, because one value lies below it and one value lies above it. Therefore, the median is 6. The median is a measure of center and is especially useful when data may be skewed or contain outliers because it depends on position rather than the magnitude of every value. The mean for this dataset is also 6, since (3 + 6 + 9) ÷ 3 = 6, but the question specifically asks for the median. Options B and C are not values in the dataset, and option D is the minimum value, not the middle. Study Guide references/topics: median, ordered data, measures of central tendency, descriptive statistics.

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