Standard Deviation Question...

[Coxx16]

 I have seen a few posts about not ever seeing 6 standard deviations. I do not quite understand why 6 standard deviations in roulette.

[Marven]

Because (when applied to a significant sample size) it's an extremely rare event.

Here you can see the normal distribution of random outcomes in terms of standard deviations (horizontal axis):



34.1% fall between 0 and 1σ (standard deviations)
13.6% fall between 1 and 2σ
and so on.

[TierPlayer]

I recall only using up to 4 std.devs when programming statistical apps.
In wikipaedia you will find  this table:

1   0.682689492137
2   0.954499736104
3   0.997300203937
4   0.999936657516
5   0.999999426697
6   0.999999998027

68% of values (see line 1 of the table) will be within 1 std.dev. away from the mean.
The "usual" 4 std.devs. will cover the 99.99% of cases (ie. only 1 in 10,000 will be outside this range)
With 6 std.devs.  the range is so wide that only 1 in 1 billion random values will fall outside.

[TierPlayer]

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