How confident is the algorithm that I am at least as good as mu - sigma?

[jauggy]

Say the algorithm knows my mu and sigma. How confident is the library that I am at least as good as mu - sigma?
And for mu-3*sigma is the algorithm close to 100% confident I am at least as good as that number?

[vivekjoshy]

$$\Pr(\mu-1\sigma \le X \le \mu+1\sigma) \approx 68.27%$$

$$\Pr(\mu-2\sigma \le X \le \mu+2\sigma) \approx 95.45%$$

$$\Pr(\mu-3\sigma \le X \le \mu+3\sigma) \approx 99.73%$$

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