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 ...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.
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 ...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.