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MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Question:** Since the area under the normal curve within two standard deviations of the mean is 0.95, the area under the normal curve that corresponds to values greater than 2 standard deviations above the mean is 0.05. - ○ True - ○ False **Explanation:** This question relates to the properties of the normal distribution. The normal distribution, often represented as a bell-shaped curve, dictates that approximately 95% of the data falls within two standard deviations from the mean in both directions (both above and below). Key Concepts: - **Standard Deviation**: A measure of the amount of variation or dispersion in a set of values. - **Mean**: The average value of a dataset. The question states that the area under the curve corresponding to values greater than two standard deviations above the mean is 0.05. Since 95% of the data falls within two standard deviations, the remaining 5% is split between the tails of the distribution, with half above and half below. Thus, the area greater than 2 standard deviations above the mean is actually 0.025 (half of 0.05), making the statement false.
Transcribed Image Text:**Question:** Since the area under the normal curve within two standard deviations of the mean is 0.95, the area under the normal curve that corresponds to values greater than 2 standard deviations above the mean is 0.05. - ○ True - ○ False **Explanation:** This question relates to the properties of the normal distribution. The normal distribution, often represented as a bell-shaped curve, dictates that approximately 95% of the data falls within two standard deviations from the mean in both directions (both above and below). Key Concepts: - **Standard Deviation**: A measure of the amount of variation or dispersion in a set of values. - **Mean**: The average value of a dataset. The question states that the area under the curve corresponding to values greater than two standard deviations above the mean is 0.05. Since 95% of the data falls within two standard deviations, the remaining 5% is split between the tails of the distribution, with half above and half below. Thus, the area greater than 2 standard deviations above the mean is actually 0.025 (half of 0.05), making the statement false.
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Normal distribution is also known as the Gaussian distribution . It is highly useful in modern day world . 

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