# Chebyshev's theorem and normal distribution

Given a normal distribution of data, we know from the Empirical Rule that in between 2 standard deviations from the mean (i.e. xbar - 2s..to..xbar + 2s) there lies about 95% of all the data.

Calculate and show the percentage of data from xbar - 2s..to..xbar + 2s using Chebyshev's theorem.

Now, if I told you that a certain data set has about 87% of the data between the data points xbar + 2s, how would you reconcile this percentage against what is known for both the Empirical Rule and what you calculated above with Chebyshev's theorem?

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#### Solution Preview

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Statistics, All Topics

Year 3

Normal distribution of data

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Given a normal distribution of data, we know from the Empirical Rule

that in between 2 standard deviations from the mean (i.e. xbar -

2s..to..xbar + 2s) ...

#### Solution Summary

The solution gives a comparison of empirical rule and Chebyshev's theorem for normal distribution.