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-9 -8 -7 -0:3- -0-2- 0:4 -0-1-

-9 -8 -7 -0:3- -0-2- 0:4 -0-1-

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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What percent of the data is less then -8%?

The image features a bell-shaped curve, commonly known as a normal distribution graph. Here's a detailed explanation suitable for an educational context: ### Graph Description: - **Curve:** The main feature is a red bell-shaped curve, representing a normal distribution. This is symmetric around its highest point at the mean, which appears to be around -6 based on the x-axis markings. - **Axes:** The x-axis ranges from -9 to -3, and the y-axis ranges from 0 to 0.4. The x-axis likely represents the data values, while the y-axis represents the probability density. - **Vertical Lines:** There are several blue and red vertical lines intersecting the curve: - **Red Line at x = -6:** This line marks the mean of the distribution. - **Blue Lines at x = -7 and x = -5:** These lines likely represent one standard deviation away from the mean on either side (±1 SD). - **Additional Blue Lines at x = -8 and x = -4:** These could represent two standard deviations away from the mean (±2 SD). ### Educational Context: This graph illustrates the properties of a normal distribution, where most of the data points cluster around the mean, and the probability of data points decreases symmetrically as you move away from the mean. The vertical lines can be used to discuss the empirical rule (68-95-99.7 rule): approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three. Understanding this graph is essential for statistical analysis, allowing students to visualize how data is spread across a range and how likely certain values are. This is particularly relevant in fields like psychology, finance, and natural sciences where data tends to be normally distributed.
Transcribed Image Text:The image features a bell-shaped curve, commonly known as a normal distribution graph. Here's a detailed explanation suitable for an educational context: ### Graph Description: - **Curve:** The main feature is a red bell-shaped curve, representing a normal distribution. This is symmetric around its highest point at the mean, which appears to be around -6 based on the x-axis markings. - **Axes:** The x-axis ranges from -9 to -3, and the y-axis ranges from 0 to 0.4. The x-axis likely represents the data values, while the y-axis represents the probability density. - **Vertical Lines:** There are several blue and red vertical lines intersecting the curve: - **Red Line at x = -6:** This line marks the mean of the distribution. - **Blue Lines at x = -7 and x = -5:** These lines likely represent one standard deviation away from the mean on either side (±1 SD). - **Additional Blue Lines at x = -8 and x = -4:** These could represent two standard deviations away from the mean (±2 SD). ### Educational Context: This graph illustrates the properties of a normal distribution, where most of the data points cluster around the mean, and the probability of data points decreases symmetrically as you move away from the mean. The vertical lines can be used to discuss the empirical rule (68-95-99.7 rule): approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three. Understanding this graph is essential for statistical analysis, allowing students to visualize how data is spread across a range and how likely certain values are. This is particularly relevant in fields like psychology, finance, and natural sciences where data tends to be normally distributed.
Expert Solution
Step 1

Given information-

Population mean, µ = -6

Population standard deviation, σ = 1

Let, X be the random variables is normally distributed.

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