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Select all the properties that must be true of a normal distribution.

Select all the properties that must be true of a normal distribution.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Properties of a Normal Distribution Select *all* the properties that must be true of a normal distribution. - ☐ The distribution is centered at the mean. - ☐ All of the data in the distribution fits within 3 standard deviations of the center of the curve. - ☐ The distribution is determined by the median and standard deviation. - ☐ The distribution is bell-shaped. - ☐ The total area under the normal distribution curve is 1 (or 100%). - ☐ The area under the normal distribution curve and within 1 standard deviation of the center is about 68% of the total area under the curve. Explanation of Diagrams: If there are any diagrams or graphs related to a normal distribution, they typically show a bell-shaped curve. This curve is symmetrical about the mean, indicating that most of the data points cluster around the central peak and the probabilities taper off equally in both directions from the mean. The diagrams may also visually represent the areas under the curve that fall within 1, 2, and 3 standard deviations from the mean, highlighting the empirical rule: - About 68% of the data lies within 1 standard deviation of the mean. - About 95% of the data lies within 2 standard deviations of the mean. - About 99.7% of the data lies within 3 standard deviations of the mean.
Transcribed Image Text:### Properties of a Normal Distribution Select *all* the properties that must be true of a normal distribution. - ☐ The distribution is centered at the mean. - ☐ All of the data in the distribution fits within 3 standard deviations of the center of the curve. - ☐ The distribution is determined by the median and standard deviation. - ☐ The distribution is bell-shaped. - ☐ The total area under the normal distribution curve is 1 (or 100%). - ☐ The area under the normal distribution curve and within 1 standard deviation of the center is about 68% of the total area under the curve. Explanation of Diagrams: If there are any diagrams or graphs related to a normal distribution, they typically show a bell-shaped curve. This curve is symmetrical about the mean, indicating that most of the data points cluster around the central peak and the probabilities taper off equally in both directions from the mean. The diagrams may also visually represent the areas under the curve that fall within 1, 2, and 3 standard deviations from the mean, highlighting the empirical rule: - About 68% of the data lies within 1 standard deviation of the mean. - About 95% of the data lies within 2 standard deviations of the mean. - About 99.7% of the data lies within 3 standard deviations of the mean.
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