The application is discussed of Johnson's transformed normal density to the distribution of skewness (√b1) and kurtosis (b2) in sampling from normal mixtures (two-components, equal variances). In particular, approximations to the distribution function of √b1(andb2) are found using the Cornish-Fisher expansion withSUas kernel. Comments on the approximations in sampling from other distributions are given, and comparisons with alternative approximations (Monte-Carlo assessments, etc.) included.