The probability that a measurement will fall within a given Closed Interval . For a continuous distribution,

(1) |

(2) |

(3) |

Now let , so . Then

(4) |

where is the so-called Erf function. The variate value producing a confidence interval CI is often denoted , so

(5) |

range | CI |

0.6826895 | |

0.9544997 | |

0.9973002 | |

0.9999366 | |

0.9999994 |

To find the standard deviation range corresponding to a given confidence interval, solve (4) for .

(6) |

CI | range |

0.800 | ± 1.28155 |

0.900 | ± 1.64485 |

0.950 | ± 1.95996 |

0.990 | ± 2.57583 |

0.995 | ± 2.80703 |

0.999 | ± 3.29053 |

© 1996-9

1999-05-26