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| Section | Objectives |
|---|---|
| Regression and Modeling | - Linear Relationships
|
| Probability Theory | - Fundamental Probability Concepts
|
| Statistical Inference | - Estimation and Confidence Intervals
|
| Descriptive Statistics | - Single Variable Data Analysis
|
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NEW QUESTION # 19
What percent of data lies within 2 standard deviations of the mean in a normal distribution?
Answer: C
Explanation:
For a normal distribution, the empirical rule, also called the 68-95-99.7 rule, describes how data are distributed around the mean. Approximately 68% of observations fall within 1 standard deviation of the mean, approximately 95% fall within 2 standard deviations, and approximately 99.7% fall within 3 standard deviations. The question asks specifically for the percentage within 2 standard deviations, so the correct value is 95%. This interval is written as # # 2# to # + 2#, where # is the mean and # is the standard deviation.
Option B corresponds to one standard deviation, not two. Option C is an imprecise version of the three- standard-deviation rule, and option D has no standard empirical-rule interpretation in this context. This rule is frequently used to estimate ranges in bell-shaped distributions. Study Guide references/topics: normal distribution, empirical rule, standard deviation, distribution spread.
NEW QUESTION # 20
Review the following inequality:
y < x # 1/2
Which shaded portion in the graphs corresponds to this inequality?
Answer: A
Explanation:
The inequality y < x # 1/2 has boundary line y = x # 1/2. This line has slope 1 and y-intercept #1/2, so it crosses the y-axis slightly below the origin and rises one unit for every one unit moved to the right. Because the inequality is strict, using " < " rather than "#," the boundary line must be dashed, showing that points on the line are not included in the solution set. The solution region must be shaded below the line because y is less than the expression x # 1/2. A useful verification method is the test point (0, 0). Substituting gives 0 < 0 #
1/2, or 0 < #1/2, which is false. Therefore, the region containing the origin should not be shaded. The fourth graph has the dashed boundary with intercept #1/2 and shades the region below the line while excluding the origin. References/topics from the Study Guide: graphing linear inequalities, slope-intercept form, dashed boundaries, test-point method.
NEW QUESTION # 21
Review the following inequality:
y # #4x + 1
Which shaded region is described by this inequality?
Answer: C
Explanation:
The inequality y # #4x + 1 has boundary line y = #4x + 1. The slope is #4, so the line must decrease steeply from left to right. The y-intercept is 1, so the line must cross the vertical axis at y = 1. Because the inequality uses "#," the boundary line must be solid, meaning points on the line are included in the solution set. The solution region must be below the line because y is less than or equal to the expression #4x + 1. A quick test point confirms this. Substitute (0, 0): 0 # #4(0) + 1, giving 0 # 1, which is true. Therefore, the shaded solution region must include the origin. Graph D shows a solid, steep downward-sloping line crossing the y-axis near 1 and shades the region containing the origin and below the boundary. References/topics from the Study Guide:
linear inequalities, slope-intercept form, boundary lines, test-point method.
NEW QUESTION # 22
Poisson mean = 4. Probability of exactly 2 events?
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