Let x and s present the sample mean and sample standard deviation, respectively. Is it possible that around 70% of data lie within x-2s and x+2s? (Yes or no)

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05-10-2021
Mathematics

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Let x and s present the sample mean and sample standard deviation, respectively. Is it possible that around 70% of data lie within x-2s and x+2s? (Yes or no)

Sagot :

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joaobezerra joaobezerra · Answer 1 · 2021-10-06T08:08:34-04:00

Using the Chebyshev's Theorem and the Empirical Rule, it is found that it is not possible that around 70% of data lie within x-2s and x+2s.

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Distributions are classified as symmetric or not symmetric.
If the distribution is not symmetric, Chebyshev's Theorem is used, which states that at least 75% of the measures are within 2 standard deviations of the mean.
If the distribution is symmetric, the Empirical Rule is used, which states that around 95% of the measures are within 2 standard deviations of the mean.

Thus, from the above bullet points, at least 75% of the measures are within x-2s and x+2s, which means that the percentage of 70% is too small.

A similar problem is given at https://brainly.com/question/23612895

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