The normalized incomplete gamma functions are defined by
where , . The author is interested in the -values that solves the following (equivalent) equations: , , where is fixed, and . This problem is of importance e.g. in probability theory and mathematical statistics. The approximations are obtained by using uniform asymptotic expansions of and in which an error function is the dominant term. Numerical results are indicated and it is shown that the method can be applied also to certain cumulative distribution functions.