### Understanding Normal Distribution: Shaded Area and Standard Deviation#### Question:The graph shows a normal distribution with a standard deviation of 10. Which percentage is the best estimate for the shaded area under this normal curve?#### Explanation:The provided graph illustrates a normal distribution, commonly known as a bell curve, with a mean (center of the curve) and the data points spread out around this mean. This particular graph has a standard deviation (a measure of the spread or dispersion of a set of data) of 10.In the graph:- The x-axis (horizontal axis) is labeled with values ranging from -50 to 10.- The y-axis (vertical axis) represents the frequency or probability density.The shaded area under the curve represents the portion of the data set that lies within a certain range of values. To determine the best estimate for the shaded area within the normal distribution, you can use the properties of the normal distribution.For a normal distribution:- About 68% of the data falls within one standard deviation (±1σ) from the mean.- About 95% of the data falls within two standard deviations (±2σ) from the mean.- About 99.7% of the data falls within three standard deviations (±3σ) from the mean.Given the standard deviation of 10:- One standard deviation (±1σ) would be from -10 to 10.- Two standard deviations (±2σ) would be from -20 to 20.- Three standard deviations (±3σ) would be from -30 to 30.Since the shaded area in the graph appears to extend from -50 to approximately -5, this includes a significant portion of the data. By estimating visually and knowing the properties of the normal distribution, it seems the shaded area likely represents one of these classic ranges. However, the provided graph predominantly shades the region starting from about -50 up to approximately the mean minus half a standard deviation. Because this is not a standard deviation point, visual estimation would place the area:Considering typical ranges, this shaded portion represents a significant coverage but less than the 99.7% range (-30 to 30), suggesting an estimate close to or possibly around 84% to 85% of the distribution.Thus, based on the visual approximation, we might estimate the shaded area under this normal curve to be around **84%** of the data distribution. Further exactifications

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Answered: 5. The graph shows a normal…

5. The graph shows a normal distribution with a standard deviation of 10. Which percentage is the best estimate for the shaded area under this normal curve? -50-45-40-35-30-25-20-15-10-6 5 10

Algebra and Trigonometry (6th Edition)

6th Edition

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Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

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