
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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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