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Use the Empirical Rule to establish an interval that includes about 95% of the observations.

Question

Use the Empirical Rule to establish an interval that includes about 95% of the observations.

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Solution

The Empirical Rule, also known as the 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data will fall within three standard deviations of the mean.

Here are the steps to establish an interval that includes about 95% of the observations:

  1. Identify the mean (μ) and standard deviation (σ) of your data set.

  2. According to the Empirical Rule, 95% of data falls within two standard deviations of the mean.

  3. To find the interval, you would calculate as follows:

    Lower limit: μ - 2σ Upper limit: μ + 2σ

This interval will contain approximately 95% of the data.

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