Approximations to inverse error functions

We have presented four approximations to the inverse cumulative distribution function of a standard normal random variable. The first two were meant purely as a tool to motivate the other approximations, although either could be useful when extreme accuracy is not required and one doesn\´t venture too far into the tails of the distribution. There are many other such "simple" approximations to F_X ^-1, suitable for use on a hand calculator.