Let X and Y be two independent continuous random variables. We make statistical inference about θ=P(X<Y), the so-called stress–strength model, through the Edgeworth expansions and the bootstrap approximations of the Studentized Wilcoxon–Mann–Whitney statistics. Finite-sample accuracy of the confidence intervals is assessed through a simulation study. Two real data sets are analysed to illustrate our methods. Copyright © 2007 John Wiley & Sons, Ltd.