The sum of those terms of the Binomial Series of for which the number of successes falls between
and is approximately

(1) |

(2) | |||

(3) | |||

(4) |

Uspensky (1937) has shown that

(5) |

(6) |

A Corollary states that the probability that successes in trials will differ
from the expected value by more than is

(7) |

(8) |

(9) |

where

(10) | |||

(11) | |||

(12) |

and

(13) |

**References**

Uspensky, J. V. *Introduction to Mathematical Probability.* New York: McGraw-Hill, 1937.

© 1996-9

1999-05-24