Normal Probability Function

[trojdor]

The primary formula listed has it's roots in Abramowitz and Stegun's
Handbook of Mathematical Functions, Tenth Printing p.932
Probability Functions 26.2.17

A modified version of this CDF approximation is used in many function libraries with good results.
(I use a similar modified approximation in my CDF programs for the HP-35s.)

However, your listing shows several typos in the constants, and that will adversely affect accuracy:

Denominator of f(t);
0.2316419 <--- your listing missing the final 9

For P(x), the constants are;
b1= 0.319381530
b2=-0.356563782
b3= 1.781477937 <--- your listing missing the extra 7 in the middle
b4=-1.821255978
b5= 1.330274429 <--- your listing has typo ... 3 as next to last digit should be 2

Additionally, modern CDF function libraries tend to replace the Sqrt(2*PI) in P(x) denominator with a pre-calculated constant, 2.50662827463, for speed / efficiency.

mike