When can one find a smooth transformation of a random variable so that the transformed random variable has a specified distribution? If the random variable is continuous, the solution is elementary; if it is discrete, it may be impossible. In this paper, a simple method is given of transforming a random variable in a smooth way to match a specified number of quantiles of an arbitrary distribution. The problem arose from a request for a simple way of transforming marks given in school assessment so that the distribution of transformed marks matches the distribution of external assessment.
