ValidVCE knows the importance of the WGU Applied-Probability-and-Statistics certification exam in the field of information technology. That is why it has prepared the remarkable WGU Applied-Probability-and-Statistics exam questions to help the aspirants pass it on the first go. The desiring candidates for the WGU Applied-Probability-and-Statistics certificate need help to find reliable Applied-Probability-and-Statistics Exam Questions study material.
| Section | Objectives |
|---|---|
| Topic 1: Statistical Inference | - Hypothesis testing
|
| Topic 2: Probability Distributions | - Discrete distributions
|
| Topic 3: Regression and Correlation | - Relationship analysis
|
| Topic 4: Probability | - Fundamental probability concepts
|
| Topic 5: Descriptive Statistics | - Data summarization
|
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NEW QUESTION # 91
Expected value of binomial X ~ B(10, 0.3) = ?
Answer: B
Explanation:
For a binomial random variable, the expected value is E(X) = np, where n is the number of trials and p is the probability of success on each trial. In this problem, X ~ B(10, 0.3), so n = 10 and p = 0.3. Substituting into the formula gives E(X) = 10 × 0.3 = 3. This means that across many repetitions of the same binomial experiment, the average number of successes would be 3. Option B, 7, would correspond to the expected number of failures if the failure probability is 0.7. Option C gives only the number of trials, not the expected successes. Option D gives only the success probability, not the expected count. The expected value combines both trial count and success probability. Study Guide references/topics: binomial distribution, expected value, success probability, discrete random variables.
NEW QUESTION # 92
A sample of 100 houses was surveyed in each of two states: Georgia and Kansas. Square footages of the houses are summarized by state in the following side-by-side box plots.
What is the interquartile range for house sizes in Georgia?
Answer: A
Explanation:
The interquartile range, or IQR, measures the spread of the middle 50% of a distribution. It is calculated as Q3
# Q1, where Q1 is the first quartile and Q3 is the third quartile. In the Georgia box plot, the left edge of the box is labeled 800, representing Q1, and the right edge of the box is labeled 2800, representing Q3. Therefore, the interquartile range is 2800 # 800 = 2000 square feet. The minimum value, 500, and maximum value, 5000, are part of the full range, not the IQR. The median, 1200, identifies the center of the distribution but is not used directly in the IQR calculation. Option D, 4500, corresponds to the full range from 500 to 5000, not the interquartile range. The correct interpretation is that the middle half of Georgia house sizes spans 2000 square feet. References/topics from the Study Guide: box plots, quartiles, interquartile range, comparing distributions.
NEW QUESTION # 93
Z-score negative #
Answer: C
Explanation:
A z-score measures how many standard deviations a data value is from the mean. The formula is z = (x # #)/#, where x is the observed value, # is the mean, and # is the standard deviation. Since standard deviation is positive, the sign of the z-score depends on the numerator, x # #. If x is less than the mean, then x # # is negative, producing a negative z-score. Therefore, a negative z-score indicates that the observed value is below the mean. A positive z-score indicates a value above the mean, while a z-score of 0 indicates a value exactly equal to the mean. Option D is incorrect because the sign of the z-score gives direct positional information relative to the mean. Study Guide references/topics: z-scores, standard normal distribution, mean, standard deviation.
NEW QUESTION # 94
Two events mutually exclusive # P(A and B) = ?
Answer: C
Explanation:
Mutually exclusive events cannot happen at the same time. Therefore, the probability of their intersection is zero: P(A and B) = 0. For instance, on a single coin toss, the event "heads" and the event "tails" are mutually exclusive because a single toss cannot produce both outcomes. Option B applies to independent events when calculating the probability of both occurring, but mutually exclusive events with positive probabilities are not independent because one event prevents the other from occurring. Option C is used to find P(A or B) for mutually exclusive events, not P(A and B). Option D would mean both events always occur together, which directly contradicts mutual exclusivity. The word "and" is the key operator: it asks for overlap. Since mutually exclusive events have no overlap, the result is 0. Study Guide references/topics: mutually exclusive events, intersections, joint probability, addition rule.
NEW QUESTION # 95
Given a normal distribution with a mean of 40 and a standard deviation of 6, what is the range that contains approximately 95% of the data?
Answer: C
Explanation:
For a normal distribution, the empirical rule states that approximately 95% of the data fall within two standard deviations of the mean. The mean is 40, and the standard deviation is 6. Two standard deviations equal 2 × 6
= 12. To construct the 95% interval, subtract and add 12 from the mean: 40 # 12 = 28 and 40 + 12 = 52.
Therefore, the range containing approximately 95% of the data is 28 to 52. Option D, 34 to 46, represents one standard deviation from the mean and corresponds to about 68% of the data. Option B, 22 to 58, represents three standard deviations from the mean and corresponds to approximately 99.7% of the data. Option C is not based on the stated standard deviation. The correct interval must be symmetric around the mean and extend exactly two standard deviations in each direction. References/topics from the Study Guide: normal distribution, empirical rule, mean, standard deviation.
NEW QUESTION # 96
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