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Which percentage is the best estimate for the shaded area under this normal curve?

Which percentage is the best estimate for the shaded area under this normal curve?

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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### Understanding Normal Distribution **Problem Statement:** The graph shows a normal distribution with a standard deviation of 10. 17. Which percentage is the best estimate for the shaded area under this normal curve? **Graph Description:** The graph represents a normal distribution, also known as a bell curve. The x-axis is marked with intervals from -50 to 10, increasing in increments of 5 units. Standard deviations from the mean are marked accordingly. A specific portion of the curve, ranging approximately from -30 to 0, is shaded. This shading highlights the area under the curve for this range of values. **Multiple Choice Options:** - A) 42.0% - B) 79.0% - C) 83.5% - D) 77.5% **Solution Explanation:** To determine which percentage is the best estimate for the shaded area, one needs to understand the properties of the normal distribution. The shaded area roughly represents the cumulative probability between -30 and 0 on the x-axis. For a normal distribution: - About 68% of the data falls within 1 standard deviation of the mean. - About 95% of the data falls within 2 standard deviations of the mean. - About 99.7% of the data falls within 3 standard deviations of the mean. Given that the shaded area appears to span between -3 standard deviations (from -30) to the mean (0), one can deduce the shaded area covers approximately half of the data within this range. This accounts for about 50% of the total distribution (since the mean divides the distribution equally). Based on this, the closest estimated value is answer choice "B) 79.0%." **Answer:** - B) 79.0%
Transcribed Image Text:### Understanding Normal Distribution **Problem Statement:** The graph shows a normal distribution with a standard deviation of 10. 17. Which percentage is the best estimate for the shaded area under this normal curve? **Graph Description:** The graph represents a normal distribution, also known as a bell curve. The x-axis is marked with intervals from -50 to 10, increasing in increments of 5 units. Standard deviations from the mean are marked accordingly. A specific portion of the curve, ranging approximately from -30 to 0, is shaded. This shading highlights the area under the curve for this range of values. **Multiple Choice Options:** - A) 42.0% - B) 79.0% - C) 83.5% - D) 77.5% **Solution Explanation:** To determine which percentage is the best estimate for the shaded area, one needs to understand the properties of the normal distribution. The shaded area roughly represents the cumulative probability between -30 and 0 on the x-axis. For a normal distribution: - About 68% of the data falls within 1 standard deviation of the mean. - About 95% of the data falls within 2 standard deviations of the mean. - About 99.7% of the data falls within 3 standard deviations of the mean. Given that the shaded area appears to span between -3 standard deviations (from -30) to the mean (0), one can deduce the shaded area covers approximately half of the data within this range. This accounts for about 50% of the total distribution (since the mean divides the distribution equally). Based on this, the closest estimated value is answer choice "B) 79.0%." **Answer:** - B) 79.0%
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