Lengths of human pregnancies have a bell-shaped distribution with mean 266 days and standard deviation 16 days. Based on the graph that is labeled through the use of the Empirical Rule, about 99.7% of human pregnancies have a length between ____ and ____ days.

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Lengths of human pregnancies have a bell-shaped distribution with mean 266 days and standard deviation 16 days.

Based on the graph that is labeled through the use of the Empirical Rule, about 99.7% of human pregnancies have a length between ____ and ____ days.

This diagram represents a normal distribution curve, often referred to as a bell curve, which is commonly used in statistics to depict the distribution of data. The diagram has the following key components:

1. **Central Mean (μ) and Standard Deviation (σ):**
   - The mean (µ) is positioned at the center of the symmetrical curve and is indicated as 266.
   - The distribution is divided into segments that represent multiples of the standard deviation (σ) away from the mean.

2. **Standard Deviation Intervals:**
   - The x-axis is segmented into intervals of standard deviations:
     - µ - 3σ: = 218
	   - µ - 2σ: = 234
	   - µ - 1σ: = 250
	   - µ + 0 (Mean):  = 266
	   - µ + 1σ: = 282 
	   - µ + 2σ: = 298
	   - µ + 3σ: = 314

3. **Percentage of Data within Intervals:**
   - Within µ ± 1σ contains approximately 68.26% of the data (34.13% on either side of the mean).
   - Within µ ± 2σ contains about 95.44% of the data, including the previous interval (adding 13.59% on each subsequential side).
   - Within µ ± 3σ holds about 99.72% of the data, inclusive of all previous intervals (adding 2.14% on each remaining side).

4. **Probabilities in the Tails:**
    - The far tails (beyond µ ± 3σ) each have approximately 0.13% of the data.

In summary, this normal distribution curve allows us to understand the dispersion of data around the mean and the likelihood of where a particular data point may lie relative to the overall distribution. The curve also highlights the empirical rule (68-95-99.7 rule), demonstrating the typical spread of data in many natural and human-made processes.
Transcribed Image Text:This diagram represents a normal distribution curve, often referred to as a bell curve, which is commonly used in statistics to depict the distribution of data. The diagram has the following key components: 1. **Central Mean (μ) and Standard Deviation (σ):** - The mean (µ) is positioned at the center of the symmetrical curve and is indicated as 266. - The distribution is divided into segments that represent multiples of the standard deviation (σ) away from the mean. 2. **Standard Deviation Intervals:** - The x-axis is segmented into intervals of standard deviations: - µ - 3σ: = 218 - µ - 2σ: = 234 - µ - 1σ: = 250 - µ + 0 (Mean): = 266 - µ + 1σ: = 282 - µ + 2σ: = 298 - µ + 3σ: = 314 3. **Percentage of Data within Intervals:** - Within µ ± 1σ contains approximately 68.26% of the data (34.13% on either side of the mean). - Within µ ± 2σ contains about 95.44% of the data, including the previous interval (adding 13.59% on each subsequential side). - Within µ ± 3σ holds about 99.72% of the data, inclusive of all previous intervals (adding 2.14% on each remaining side). 4. **Probabilities in the Tails:** - The far tails (beyond µ ± 3σ) each have approximately 0.13% of the data. In summary, this normal distribution curve allows us to understand the dispersion of data around the mean and the likelihood of where a particular data point may lie relative to the overall distribution. The curve also highlights the empirical rule (68-95-99.7 rule), demonstrating the typical spread of data in many natural and human-made processes.
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