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After learning about the empirical rule / $68-95-99.7$ rule, I am just wondering about the percentage of values $4$ standard deviations from the mean.
This question is pretty much the same as the Percentage of values between $3$ standard deviations and $4$ standard deviations.

I know this will be clearly less than $0.15\%$. If anyone answers, their help will be appreciated.

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    $\begingroup$ The value is $99.99366575$% $\endgroup$
    – Peter
    Commented May 3 at 7:11
  • $\begingroup$ @Peter Thank you. $\endgroup$
    – GSmith
    Commented May 3 at 7:16
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    $\begingroup$ I know what you indicate , @Peter , though the number OP is wanting here is very small. $\endgroup$
    – Prem
    Commented May 3 at 15:27

1 Answer 1

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According to https://blog.masterofproject.com/six-sigma-statistics/ :

$\pm 1 \sigma : 68\%$
$\pm 2 \sigma : 95\%$
$\pm 3 \sigma : 99.73\%$
$\pm 4 \sigma : 99.9937\%$
$\pm 5 \sigma : 99.99994\%$
$\pm 6 \sigma : 99.9999998\%$

Hence , Percentage of values between $\pm 3 \sigma$ & $\pm 4 \sigma$ is :
$$99.9937\%-99.73\% \approx 0.2637\%$$

Pictorially :

123456

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  • $\begingroup$ Is there a formula for this, or are these values just known? $\endgroup$
    – GSmith
    Commented May 4 at 7:13
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    $\begingroup$ There is no simple easy formula. Similar to trig tables & log tables , there are accurate tables ( earlier generated manually & now generated with Computers ) which we have to use in Statistics. $\endgroup$
    – Prem
    Commented May 4 at 8:46
  • $\begingroup$ Thank you for the help! $\endgroup$
    – GSmith
    Commented May 25 at 9:42

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