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Sketch a bell curve for the SAT mathematics data with markings on the horizontal axis for ±1 standard deviation, ±2 standard deviations, and ±3 standard deviations.

Sketch a bell curve for the SAT mathematics data with markings on the horizontal axis for ±1 standard deviation, ±2 standard deviations, and ±3 standard deviations.

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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**Sketch a Bell Curve for SAT Mathematics Data** To create a bell curve (normal distribution) for the SAT mathematics data, you'll need to mark the horizontal axis with the standard deviations from the mean. Below are the detailed instructions: 1. **Draw the Axes:** - Draw a horizontal line to represent the x-axis, which will correspond to SAT mathematics scores. - Draw a vertical line to represent the y-axis, which will correspond to the frequency or probability of the scores. 2. **Mark the Mean:** - Identify and mark the mean (average) SAT mathematics score on the x-axis. This is the highest point of the bell curve and is typically denoted as μ. 3. **Mark Standard Deviations:** - You need to mark ±1, ±2, and ±3 standard deviations (σ) from the mean on the horizontal axis. - These points represent how scores are distributed around the mean. 4. **Sketch the Bell Curve:** - Draw a symmetrical bell-shaped curve centered at the mean. It should touch the x-axis at both ends and peak at the mean. - Label the points at the mean, ±1σ, ±2σ, and ±3σ. **Explanation of the Bell Curve:** - The area under the bell curve represents the total probability and is equal to 1. - Approximately 68% of the data lies within ±1 standard deviation (σ) from the mean. - Approximately 95% of the data lies within ±2σ. - Approximately 99.7% of the data lies within ±3σ. This sketch helps to visualize how SAT mathematics scores are distributed among students, providing insights into the average performance and the variability of scores.
Transcribed Image Text:**Sketch a Bell Curve for SAT Mathematics Data** To create a bell curve (normal distribution) for the SAT mathematics data, you'll need to mark the horizontal axis with the standard deviations from the mean. Below are the detailed instructions: 1. **Draw the Axes:** - Draw a horizontal line to represent the x-axis, which will correspond to SAT mathematics scores. - Draw a vertical line to represent the y-axis, which will correspond to the frequency or probability of the scores. 2. **Mark the Mean:** - Identify and mark the mean (average) SAT mathematics score on the x-axis. This is the highest point of the bell curve and is typically denoted as μ. 3. **Mark Standard Deviations:** - You need to mark ±1, ±2, and ±3 standard deviations (σ) from the mean on the horizontal axis. - These points represent how scores are distributed around the mean. 4. **Sketch the Bell Curve:** - Draw a symmetrical bell-shaped curve centered at the mean. It should touch the x-axis at both ends and peak at the mean. - Label the points at the mean, ±1σ, ±2σ, and ±3σ. **Explanation of the Bell Curve:** - The area under the bell curve represents the total probability and is equal to 1. - Approximately 68% of the data lies within ±1 standard deviation (σ) from the mean. - Approximately 95% of the data lies within ±2σ. - Approximately 99.7% of the data lies within ±3σ. This sketch helps to visualize how SAT mathematics scores are distributed among students, providing insights into the average performance and the variability of scores.
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