Questions: - Approximately 68 percent of the data are within one standard deviation ( σ ) of the mean ( μ ). - Approximately 95 percent of the data are within two standard deviations ( σ ) of the mean ( μ ). - Approximately 99.7 percent of the data are within three standard deviations (σ) of the mean (μ). 2. The mean of people 65 and older in populations across all U.S. counties is 18% and the interval and the percentage of data each comprises, based on the normal approximation of those values. In other words, label the intervals with the percentages of the curve they represent. Each interval will have a value.

- Approximately 68 percent of the data are within one standard deviation ( σ ) of the mean ( μ ).
- Approximately 95 percent of the data are within two standard deviations ( σ ) of the mean ( μ ).
- Approximately 99.7 percent of the data are within three standard deviations (σ) of the mean (μ).
2. The mean of people 65 and older in populations across all U.S. counties is 18% and the interval and the percentage of data each comprises, based on the normal approximation of those values. In other words, label the intervals with the percentages of the curve they represent. Each interval will have a value.
Transcript text: - Approximately 68 percent of the data are within one standard deviation ( $\sigma$ ) of the mean ( $\mu$ ). - Approximately 95 percent of the data are within two standard deviations ( $\sigma$ ) of the mean ( $\mu$ ). - Approximately 99.7 percent of the data are within three standard deviations $(\sigma)$ of the mean $(\mu)$. 2. The mean of people 65 and older in populations across all U.S. counties is $18 \%$ and the interval and the percentage of data each comprises, based on the normal approximation of those values. In other words, label the intervals with the percentages of the curve they represent. Each interval will have a value.
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Solution

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Solution Steps

Step 1: Calculate one standard deviation from the mean

The mean (μ) is 18% and the standard deviation (σ) is 4%. One standard deviation from the mean is μ ± σ, which is 18 ± 4. Thus, the interval is (14%, 22%). This corresponds to 68% of the data.

Step 2: Calculate two standard deviations from the mean

Two standard deviations from the mean is μ ± 2σ, which is 18 ± 2 * 4. This gives us the interval (10%, 26%). This corresponds to 95% of the data.

Step 3: Calculate three standard deviations from the mean

Three standard deviations from the mean is μ ± 3σ, which is 18 ± 3 * 4. This gives us the interval (6%, 30%). This corresponds to 99.7% of the data.

Final Answer:

  • μ - 3σ to μ - 2σ: 6% to 10% (2.15% of the data)
  • μ - 2σ to μ - σ: 10% to 14% (13.5% of the data)
  • μ - σ to μ: 14% to 18% (34% of the data)
  • μ to μ + σ: 18% to 22% (34% of the data)
  • μ + σ to μ + 2σ: 22% to 26% (13.5% of the data)
  • μ + 2σ to μ + 3σ: 26% to 30% (2.15% of the data)
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