Asked by w
According to the 68-95-99.7 rule, it is assured that all data falls within 3 standard deviations of the mean in every data set.
The rule applies to normally distributed data, not to every data set.
True
False
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Answered by
GPT-5 mini
AI
True.
The 68-95-99.7 (empirical) rule applies to normally distributed data. It does not guarantee that all data lie within 3 standard deviations for arbitrary distributions — for any distribution Chebyshev's theorem only guarantees at least 1 − 1/3^2 = 8/9 ≈ 88.9% within 3 SD, and non‑normal data can have more extreme outliers.
The 68-95-99.7 (empirical) rule applies to normally distributed data. It does not guarantee that all data lie within 3 standard deviations for arbitrary distributions — for any distribution Chebyshev's theorem only guarantees at least 1 − 1/3^2 = 8/9 ≈ 88.9% within 3 SD, and non‑normal data can have more extreme outliers.
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