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Six Sigma - What it means

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Please clarify this statement:

If you look at the probability of attaining 6 sigma (2 parts per billion), what does this say when the .400 batting average is at least 6 sigma from the mean?

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The concept of Six Sigma explained briefly and the given statement has been interpreted.

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The  limits are generally used in statistical process controls to specify how much deviation is allowed from the mean process specifications.
1  means a deviation of plus or minus one standard deviation from the mean value is allowed (or was achieved in a process). This has a probability of 0.6827, which means a failure rate of 31.73%.
2 ...

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