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The contents of Applied-Probability-and-Statistics study materials are all compiled by industry experts based on the Applied-Probability-and-Statistics examination outlines and industry development trends over the years. It does not overlap with the content of the Applied-Probability-and-Statistics question banks on the market, and avoids the fatigue caused by repeated exercises. Our Applied-Probability-and-Statistics Exam Guide is not simply a patchwork of exam questions, but has its own system and levels of hierarchy, which can make users improve effectively.
| Section | Objectives |
|---|---|
| Topic 1: Descriptive Statistics | - Data summarization
|
| Topic 2: Statistical Inference | - Hypothesis testing
|
| Topic 3: Regression and Correlation | - Relationship analysis
|
| Topic 4: Probability Distributions | - Continuous distributions
|
| Topic 5: Probability | - Probability rules
|
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NEW QUESTION # 15
68-95-99.7 rule: % within 1 SD?
Answer: D
Explanation:
The 68-95-99.7 rule, also called the empirical rule, applies to approximately normal distributions. It states that about 68% of observations fall within 1 standard deviation of the mean, about 95% fall within 2 standard deviations, and about 99.7% fall within 3 standard deviations. The question asks specifically for the percentage within 1 standard deviation, so the correct answer is 68%. In notation, this interval is # # # to # +
#, where # is the mean and # is the standard deviation. This rule is useful for interpreting spread in bell- shaped distributions. For example, if scores have mean 80 and standard deviation 5, then approximately 68% of scores fall between 75 and 85. Option B corresponds to 2 standard deviations, and option C corresponds approximately to 3 standard deviations. Option D is not part of the empirical rule. Study Guide references
/topics: empirical rule, normal distribution, standard deviation, spread.
NEW QUESTION # 16
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: D
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 # 17
A child's parents want to analyze the relationship between the daily high temperature and ice cream sales at their child's ice cream stand. They create the following scatterplot.
What is the estimated value of r, the correlation coefficient, between these variables?
Answer: A
Explanation:
The correlation coefficient r measures both the direction and strength of a linear relationship between two quantitative variables. In this scatterplot, the points rise from lower left to upper right, showing a positive association between temperature and daily ice cream sales. As temperature increases, sales also tend to increase. The points are fairly close to an upward-sloping linear pattern, so the relationship is strong rather than weak. A value of r near 1 indicates a strong positive linear association, while a value near #1 indicates a strong negative association. Since the association is clearly positive, the negative options, #0.93 and #0.39, are not appropriate. Since the points show a strong trend rather than a loose or weak trend, 0.39 is too small.
The best estimate is 0.93. This is consistent with the visual pattern: temperature explains a substantial amount of the linear movement in ice cream sales. References/topics from the Study Guide: scatterplots, correlation coefficient, positive association, strength of linear relationship.
NEW QUESTION # 18
What is the product of 0.6 and 0.25?
Answer: C
Explanation:
To multiply decimals, first multiply the numbers as whole numbers and then place the decimal point according to the total number of decimal places in the factors. The values are 0.6 and 0.25. Ignoring decimals temporarily, 6 × 25 = 150. The factor 0.6 has one decimal place, and 0.25 has two decimal places, for a total of three decimal places. Therefore, 150 becomes 0.150, which is equivalent to 0.15. A second way to verify the computation is to convert the decimals into fractions: 0.6 = 6/10 and 0.25 = 25/100. Multiplying gives (6 ×
25)/(10 × 100) = 150/1000 = 0.15. This result is reasonable because one-fourth of 0.6 is 0.15. The other answer choices are too large for one-fourth of 0.6 or do not result from the correct decimal multiplication.
References/topics from the Study Guide: decimal multiplication, fractions, equivalent forms, numerical operations.
NEW QUESTION # 19
The pie chart shows the contribution of different renewable energy sources to the total energy production.
What is true about the given data?
Answer: D
Explanation:
A pie chart displays how a whole is divided into categorical parts, usually as percentages totaling 100%. The chart shows solar at 35%, hydropower at 30%, wind at 20%, geothermal at 10%, and biomass at 5%. The largest percentage is solar, so solar power contributes the most to total energy production. Option A is false because hydropower plus biomass equals 30% + 5% = 35%, which is equal to solar, not more than solar.
Option B is false because geothermal is 10%, while biomass is only 5%; therefore, biomass contributes the least. Option C is false because biomass plus geothermal equals 5% + 10% = 15%, which is less than wind at
20%. The correct interpretation requires comparing category percentages accurately rather than relying on visual size alone. References/topics from the Study Guide: pie charts, categorical data, percentages, interpreting graphical displays.
NEW QUESTION # 20
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