For the normal cumulative distribution function: Φ(x) we give the
new approximation 2**(-22**(1-41**(x/10))) for any x>0, which is very
simple (with only integer constants and operations - and / and power
elevation **) and is very simply explicitly invertible having 1 entry of x.
It has 3 decimals of precision having absolute error less than 0.00013. We
compute the inverse which approximates the normal quantile function,
or probit, and it has the relative precision of 1 percent (from 0.5) till
beyond 0.999. We give an open problem and a noticeable bibliography.
We report several other approximations.
