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- https://biz.libretexts.org/Workbench/MGT_235/06%3A_Confidence_Intervals/6.01%3A_IntroductionThe empirical rule, which applies to the normal distribution, says that in approximately 95% of the samples, the sample mean, \(\overline x\), will be within two standard deviations of the population ...The empirical rule, which applies to the normal distribution, says that in approximately 95% of the samples, the sample mean, \(\overline x\), will be within two standard deviations of the population mean \mu. Where \(\overline x\) is the sample mean. \(Z_{\alpha}\) is determined by the level of confidence desired by the analyst, and \(\sigma / \sqrt{n}\) is the standard deviation of the sampling distribution for means given to us by the Central Limit Theorem.
- https://biz.libretexts.org/Courses/Gettysburg_College/MGT_235%3A_Introductory_Business_Statistics_(2nd_edition)/04%3A_The_Normal_Distribution/4.02%3A_The_Standard_Normal_DistributionThe z-score tells you how many standard deviations the value \(\bf{x}\) is above (to the right of) or below (to the left of) the mean, \(\bf{\mu}\). About 95% of the \(x\) values lie between \(–2\sigm...The z-score tells you how many standard deviations the value \(\bf{x}\) is above (to the right of) or below (to the left of) the mean, \(\bf{\mu}\). About 95% of the \(x\) values lie between \(–2\sigma\) and \(+2\sigma\) of the mean \(\mu\) (within two standard deviations of the mean). About 99.7% of the \(x\) values lie between \(–3\sigma\) and \(+3\sigma\) of the mean \(\mu\) (within three standard deviations of the mean).
- https://biz.libretexts.org/Courses/Gettysburg_College/MGT_235%3A_Introductory_Business_Statistics_(2nd_edition)/06%3A_Confidence_Intervals/6.01%3A_IntroductionThe empirical rule, which applies to the normal distribution, says that in approximately 95% of the samples, the sample mean, \(\overline x\), will be within two standard deviations of the population ...The empirical rule, which applies to the normal distribution, says that in approximately 95% of the samples, the sample mean, \(\overline x\), will be within two standard deviations of the population mean \(\mu\). Where \(\overline x\) is the sample mean. \(z_\frac{\alpha}{2}\) is determined by the level of confidence (1-\(\alpha\)) desired by the analyst, and \(s / \sqrt{n}\) is the standard deviation of the sampling distribution for means given to us by the Central Limit Theorem.
- https://biz.libretexts.org/Workbench/MGT_235/04%3A_The_Normal_Distribution/4.02%3A_The_Standard_Normal_DistributionThe z-score tells you how many standard deviations the value \(\bf{x}\) is above (to the right of) or below (to the left of) the mean, \(\bf{\mu}\).Values of \(x\) that are larger than the mean have p...The z-score tells you how many standard deviations the value \(\bf{x}\) is above (to the right of) or below (to the left of) the mean, \(\bf{\mu}\).Values of \(x\) that are larger than the mean have positive z-scores, and values of \(x\) that are smaller than the mean have negative z-scores. About 95% of the \(x\) values lie between \(–2\sigma\) and \(+2\sigma\) of the mean \(\mu\) (within two standard deviations of the mean).
