Answer:
A bell curve representing the mean pulse rates of samples of size 2553. Labeled points include the mean (μ), one standard deviation from the mean (±σ), two standard deviations from the mean (±2σ), and three standard deviations from the mean (±3σ). Use the 68-95-99.7 Rule to show that approximately 68% of the data falls within one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations of the mean.
Step-by-step explanation:
The 68-95-99.7 Rule, also known as the Empirical Rule or Three Sigma Rule, provides a way to understand the spread of data in a normal distribution.
It states that:
- Approximately 68% of the data falls within one standard deviation (σ) of the mean (μ).
- Approximately 95% falls within two standard deviations (2σ) of the mean.
- Approximately 99.7% falls within three standard deviations (3σ) of the mean.
Assuming a normal distribution for the mean pulse rates of samples of size 2553, you can sketch a bell curve (normal distribution curve) with the following labels:
- Mean (μ): The center of the curve.
- σ: One standard deviation from the mean on both sides.
- 2σ: Two standard deviations from the mean on both sides.
- 3σ: Three standard deviations from the mean on both sides.
Here's a textual representation:
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μ μ+σ μ+2σ μ+3σ μ-σ μ-2σ μ-3σ
This represents a bell curve where the majority of data falls within ±1σ, ±2σ, and ±3σ from the mean.
You can label the regions accordingly based on the percentages given by the 68-95-99.7 Rule.