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3. Determine the location of the tails for the distribution

The next step is to determine where (at what value) the tails or ends of the curve are located. These values can be estimated by adding and subtracting three times the estimated standard deviation from the overall average. Remember, from the histogram section, that for a normal distribution, plus or minus three times the standard deviation from the overall average includes 99.73 percent of the area under the curve.

The calculation for the location of the left tail is:

For the example the left tail is:

The right tail is calculated as follows:

For the example the right tail is:

Add the values to the distribution drawn earlier. The example completed through this step follows.

The above article is an excerpt from the "Operational definition" chapter of Practical Tools for Continuous Improvement Volume 2 Statistical Tools.

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