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Choose the statement(s) which is/are true of a normal distribution. 1. The graph of a normal distribution is symmetric about the mean. 2. The shape of the graph of a normal distribution is bell-shaped. 3. 99.7% of the data is within 2 standard deviations of the center. 2 only 1 only 1 and 3 only 3 only 1 and 2 only

Choose the statement(s) which is/are true of a normal distribution. 1. The graph of a normal distribution is symmetric about the mean. 2. The shape of the graph of a normal distribution is bell-shaped. 3. 99.7% of the data is within 2 standard deviations of the center. 2 only 1 only 1 and 3 only 3 only 1 and 2 only

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Understanding Normal Distribution** **Choose the statement(s) which is/are true of a normal distribution:** 1. The graph of a normal distribution is symmetric about the mean. 2. The shape of the graph of a normal distribution is bell-shaped. 3. 99.7% of the data is within 2 standard deviations of the center. **Options:** ○ 2 only ○ 1 only ○ 1 and 3 only ○ 3 only ○ 1 and 2 only **Explanation:** To analyze the given statements, let's understand some fundamental characteristics of a normal distribution: 1. **Symmetry**: The graph of a normal distribution is symmetric about the mean. This means that the left side of the graph is a mirror image of the right side. 2. **Shape**: The shape of the graph of a normal distribution is bell-shaped. This indicates that it has a single peak (mean) and gradually decreases on both sides. 3. **Empirical Rule**: According to the empirical rule, for a normal distribution: - About 68.3% of data falls within 1 standard deviation of the mean. - About 95.4% of data falls within 2 standard deviations of the mean. - About 99.7% of data falls within 3 standard deviations of the mean. **Correct Answer:** ○ 1 and 2 only **Explanation of Graphs/Diagrams:** A graph of a normal distribution typically shows a symmetric bell-shaped curve. The center represents the mean, and the curve extends infinitely in both directions, approaching but never touching the horizontal axis. The peak of the bell curve represents the highest frequency of data points, and the symmetry about the mean indicates that for any deviation in one direction, there is an equal deviation in the opposite direction.
Transcribed Image Text:**Understanding Normal Distribution** **Choose the statement(s) which is/are true of a normal distribution:** 1. The graph of a normal distribution is symmetric about the mean. 2. The shape of the graph of a normal distribution is bell-shaped. 3. 99.7% of the data is within 2 standard deviations of the center. **Options:** ○ 2 only ○ 1 only ○ 1 and 3 only ○ 3 only ○ 1 and 2 only **Explanation:** To analyze the given statements, let's understand some fundamental characteristics of a normal distribution: 1. **Symmetry**: The graph of a normal distribution is symmetric about the mean. This means that the left side of the graph is a mirror image of the right side. 2. **Shape**: The shape of the graph of a normal distribution is bell-shaped. This indicates that it has a single peak (mean) and gradually decreases on both sides. 3. **Empirical Rule**: According to the empirical rule, for a normal distribution: - About 68.3% of data falls within 1 standard deviation of the mean. - About 95.4% of data falls within 2 standard deviations of the mean. - About 99.7% of data falls within 3 standard deviations of the mean. **Correct Answer:** ○ 1 and 2 only **Explanation of Graphs/Diagrams:** A graph of a normal distribution typically shows a symmetric bell-shaped curve. The center represents the mean, and the curve extends infinitely in both directions, approaching but never touching the horizontal axis. The peak of the bell curve represents the highest frequency of data points, and the symmetry about the mean indicates that for any deviation in one direction, there is an equal deviation in the opposite direction.
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