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Determine whether the following graph can represent a normal curve. 0-

Determine whether the following graph can represent a normal curve. 0-

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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**Graph Analysis for Normal Curve Determination** The image presents a graph for analysis to determine if it represents a normal curve. **Graph Details:** - The graph features two axes: a vertical axis (presumably the y-axis) and a horizontal axis labeled with "x." - Initial observation shows the curve starting at the origin (0 on the y-axis) and rising sharply, forming a peak before descending in a similar sharp manner below the x-axis. - The curve ascends above the x-axis and then dips below it after reaching its peak, indicating a symmetric bell-shaped form but crossing the x-axis, which is not characteristic of a standard normal distribution curve. **Key Characteristics of a Normal Curve:** 1. **Shape**: A normal curve is bell-shaped and symmetrical concerning the mean. 2. **Position**: It does not cross the x-axis; it asymptotically approaches but never touches the x-axis. 3. **Area**: The total area under the curve equals 1, representing the entire probability distribution. 4. **Axis Symmetry**: The highest point is at the mean. **Conclusion:** While the graph demonstrates symmetry resembling a bell-shaped curve, the fact that it crosses the x-axis disqualifies it from being a standard normal distribution curve. Normal curves should never intersect or dip below the x-axis and must maintain symmetry around the mean.
Transcribed Image Text:**Graph Analysis for Normal Curve Determination** The image presents a graph for analysis to determine if it represents a normal curve. **Graph Details:** - The graph features two axes: a vertical axis (presumably the y-axis) and a horizontal axis labeled with "x." - Initial observation shows the curve starting at the origin (0 on the y-axis) and rising sharply, forming a peak before descending in a similar sharp manner below the x-axis. - The curve ascends above the x-axis and then dips below it after reaching its peak, indicating a symmetric bell-shaped form but crossing the x-axis, which is not characteristic of a standard normal distribution curve. **Key Characteristics of a Normal Curve:** 1. **Shape**: A normal curve is bell-shaped and symmetrical concerning the mean. 2. **Position**: It does not cross the x-axis; it asymptotically approaches but never touches the x-axis. 3. **Area**: The total area under the curve equals 1, representing the entire probability distribution. 4. **Axis Symmetry**: The highest point is at the mean. **Conclusion:** While the graph demonstrates symmetry resembling a bell-shaped curve, the fact that it crosses the x-axis disqualifies it from being a standard normal distribution curve. Normal curves should never intersect or dip below the x-axis and must maintain symmetry around the mean.
**Could the graph represent a normal curve? Select all that apply.** - **A.** No, because the graph is always greater than or equal to zero. - **B.** No, because the graph is symmetric about its mean. - **C.** No, because the highest point of the graph occurs at the mean. - **D.** Yes, because the graph satisfies all of the criteria for a normal curve. - **E.** No, because the highest point of the graph does not occur at the median. - **F.** No, because the graph has multiple peaks. - **G.** No, because the graph is not symmetric about its mean. - **H.** Yes, because the graph may not satisfy all of the criteria for a normal curve, but it satisfies at least one of the criteria. - **I.** No, because the graph is not always greater than or equal to zero. - **J.** No, because the graph has a single peak.
Transcribed Image Text:**Could the graph represent a normal curve? Select all that apply.** - **A.** No, because the graph is always greater than or equal to zero. - **B.** No, because the graph is symmetric about its mean. - **C.** No, because the highest point of the graph occurs at the mean. - **D.** Yes, because the graph satisfies all of the criteria for a normal curve. - **E.** No, because the highest point of the graph does not occur at the median. - **F.** No, because the graph has multiple peaks. - **G.** No, because the graph is not symmetric about its mean. - **H.** Yes, because the graph may not satisfy all of the criteria for a normal curve, but it satisfies at least one of the criteria. - **I.** No, because the graph is not always greater than or equal to zero. - **J.** No, because the graph has a single peak.
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