## de Moivre-Laplace Theorem

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

 (1)

where
 (2) (3) (4)

Uspensky (1937) has shown that

 (5)

where
 (6)

for .

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

 (7)

where
 (8)

Uspensky (1937) showed that
 (9)

where
 (10) (11) (12)

and
 (13)

for .

References

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