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If observations from an experiment are normally distributed, what percentage of the observations differ from the mean by more than $1.3\sigma$ where $\sigma$ is the standard deviation.

Would it be $P(X-\mu > 1.3\sigma)$? Or do I have to look at the other side of the distribution as well?

Lemon
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1 Answers1

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Both sides have to be looked at. Or use symmetry, do one side only and double.

André Nicolas
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  • So $2P(X-\mu > 1.3\sigma)$? Because for some reason I have $0.1972$ and this http://www.brinkmann-du.de/mathe/gost/stoch_01_14.htm site says $1.3\sigma$ corresponds to 0.806 – Lemon Jul 30 '13 at 05:33
  • My table gives that the right tail has probability $0.0968$, double to get $01936$, that is, $19.36%$ (the question asks for a percent). The site you point to calculates the probability that $|X-\mu|\le k\sigma$, so not the tail but the middle, which of course is $1$ minus the number we want. – André Nicolas Jul 30 '13 at 05:42