Which of the distributions shown has the smallest standard deviation? e: O The green curve, because its peak is furthest to the left on the number line. O The black curve, because it is the widest. O The red curve, because it is between the other two curves. The green curve, because it is the narrowest.

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**Which of the distributions shown has the smallest standard deviation?**

**Choose One:**
1. 
    - O The green curve, because its peak is furthest to the left on the number line.
2. 
    - O The black curve, because it is the widest.
3. 
    - O The red curve, because it is between the other two curves.
4. 
    - O The green curve, because it is the narrowest.

**Explanation of Graphs and Diagrams:**
The image shows a graph with three different curves, each representing a probability distribution:

- **Green Curve:** This curve is the narrowest and has the highest peak among the three. The narrowness of this curve indicates a smaller standard deviation.
- **Red Curve:** This curve is wider than the green curve but narrower than the black curve. It sits in between the two extremes in terms of standard deviation.
- **Black Curve:** This curve is the widest and has the lowest peak among the three. The width of this curve indicates the largest standard deviation.

Standard deviation is a measure of the amount of variation or dispersion in a set of values. The narrower the curve, the smaller the standard deviation, as the data points are closer to the mean. Conversely, the wider the curve, the larger the standard deviation, indicating that the data points are more spread out from the mean.
Transcribed Image Text:**Which of the distributions shown has the smallest standard deviation?** **Choose One:** 1. - O The green curve, because its peak is furthest to the left on the number line. 2. - O The black curve, because it is the widest. 3. - O The red curve, because it is between the other two curves. 4. - O The green curve, because it is the narrowest. **Explanation of Graphs and Diagrams:** The image shows a graph with three different curves, each representing a probability distribution: - **Green Curve:** This curve is the narrowest and has the highest peak among the three. The narrowness of this curve indicates a smaller standard deviation. - **Red Curve:** This curve is wider than the green curve but narrower than the black curve. It sits in between the two extremes in terms of standard deviation. - **Black Curve:** This curve is the widest and has the lowest peak among the three. The width of this curve indicates the largest standard deviation. Standard deviation is a measure of the amount of variation or dispersion in a set of values. The narrower the curve, the smaller the standard deviation, as the data points are closer to the mean. Conversely, the wider the curve, the larger the standard deviation, indicating that the data points are more spread out from the mean.
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