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| Section | Objectives |
|---|---|
| Topic 1: Descriptive Statistics | - Single Variable Data Analysis
|
| Topic 2: Probability Theory | - Fundamental Probability Concepts
|
| Topic 3: Regression and Modeling | - Linear Relationships
|
| Topic 4: Statistical Inference | - Estimation and Confidence Intervals
|
>> WGU Applied-Probability-and-Statistics Lernhilfe <<
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147. Frage
A road safety research group wants to enhance road safety by analyzing the stopping distance of a car at different speeds. The group has recorded their data in the following scatterplot.
What is true about the outlier in the scatterplot?
Antwort: D
Begründung:
An outlier is a data point that does not follow the general pattern of the remaining data. In this scatterplot, most points show a clear increasing relationship: as speed increases, stopping distance also increases. The main cluster follows a smooth upward trend, with stopping distances gradually rising as speed increases. One point, however, is far above the rest of the pattern. That point is located at approximately 40 mph and 560 feet, making it unusually high compared with the expected stopping distance at that speed. This is why option D correctly identifies the outlier. Option A describes a low-speed point that fits the lower end of the trend.
Option B describes a high-speed point near the upper end of the general pattern, not an unusual deviation.
Option C describes a point around 30 mph and 190 feet, which lies within the main cluster of observations.
The outlier is not merely an extreme x-value or y-value; it is unusual relative to the trend. References/topics from the Study Guide: scatterplots, outliers, bivariate data, association patterns.
148. Frage
There are 14 black, 16 white, and 10 red balls in a box.
What is the probability of selecting 1 black ball, then 1 red ball, and then 1 white ball, replacing the ball each time?
Antwort: D
Begründung:
The box contains 14 black, 16 white, and 10 red balls, for a total of 40 balls. Because the ball is replaced after each selection, the probability of each color remains constant on every draw. This makes the three draws independent. The probability of selecting a black ball first is 14/40, which simplifies to 7/20. The probability of selecting a red ball second is 10/40, or 1/4. The probability of selecting a white ball third is 16/40, or 2/5.
Since the question asks for all three events in the stated order, multiply the probabilities: (7/20)(1/4)(2/5) = 14
/400 = 7/200. Replacement is the controlling condition; without replacement, the denominators would decrease after each draw. Here, the sample space remains 40 each time. References/topics from the Study Guide: probability, independent events, replacement, multiplication rule.
149. Frage
A study recorded the number of hours participants spent on exercise per week: 3 participants exercised for 1 hour, 6 participants exercised for 2 hours, 4 participants exercised for 3 hours, and 2 participants exercised for
4 hours.
Which type of graph would best represent the frequency of exercise hours?
Antwort: A
Begründung:
The data describe frequencies for a single variable: weekly exercise duration. Each duration, 1 hour through 4 hours, has an associated count of participants. A bar chart is the most appropriate display because it uses separate bars to show how many observations fall into each category or discrete value. Here, the bar above 1 hour would have height 3, the bar above 2 hours would have height 6, the bar above 3 hours would have height 4, and the bar above 4 hours would have height 2. A line graph is inappropriate because the data are not measuring change over time. A pie chart could show proportions, but the question specifically asks for frequency of exercise hours, making a bar chart clearer and more direct. A scatterplot requires two quantitative variables and is used to study association, not a one-variable frequency distribution. References
/topics from the Study Guide: frequency distributions, bar charts, single-variable data displays, quantitative
/discrete data.
150. Frage
A class of 25 students includes 10 who play soccer, 8 who play basketball, and 7 who play neither sport.
What is the probability of randomly selecting a student who does not play soccer?
Antwort: D
Begründung:
The probability of selecting a student who does not play soccer is found by identifying the complement of the soccer group. There are 25 students in the class, and 10 students play soccer. Therefore, the number of students who do not play soccer is 25 # 10 = 15. The probability is then the number of favorable outcomes divided by the total number of possible outcomes: 15/25 = 0.60. The information about basketball and neither sport provides context, but the direct complement method is sufficient because the question asks only who does not play soccer. Option B, .40, represents the probability of selecting a student who does play soccer, since 10/25 = .40. Option A, .30, is associated with neither sport if interpreted approximately from 7/25, but it is not the requested event. Option C, .50, does not match the count structure. References/topics from the Study Guide: probability, complements, favorable outcomes, relative frequency.
151. Frage
A home inspector finds 3% of the homes in a community infected with termites.
How should the home inspector's findings be interpreted?
Antwort: C
Begründung:
A probability or percentage describes how often an event is expected to occur in the long run. Here, 3% of homes are infected with termites. As a probability, this is 0.03, meaning about 3 out of every 100 homes would be expected to have termites. This is a small probability, so the event should be interpreted as unlikely.
It is not impossible, because impossible would require a probability of 0%. It is also not likely, because likely events generally have probabilities substantially greater than 50%. Finally, it is not "as likely as unlikely," because that language corresponds to a probability near 50%, where occurrence and nonoccurrence are approximately balanced. Since 3% is close to zero but not equal to zero, the technically correct interpretation is that termite infection is unlikely for a randomly selected home in the community. References/topics from the Study Guide: probability interpretation, percentages, unlikely events, complementary probability.
152. Frage
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