Inverting the Normal Distribution Suppose F(x) is the standard normal distribution function. Construct a rough approximation G(u) to F −1(u) for 0.5 ≤ u < 1 as follows:

a) Construct a rational function G(u) (−→ Appendix C1) with correct asymptotic behavior, point symmetry with respect to (u, x) = (0.5, 0), using only one parameter.

b) Fix the parameter by interpolating a given point (x1, F(x1)).

c) What is a simple criterion for the error of the approximation?