A population projection is a prediction of a random vector variable XT. which represents the size and age/sex distribution of the population in year T. The population is assumed to be closed and to develop according to fixed and known schedules of birth and death probabilities as a multitype branching process. The precision of the usual projection eT(= EXT) is studied by a family of prediction intervals of linear functions of the vector of deviations XT — eT, which has a preassigned probability level. This family is obtained by a multi-normal approximation and an argument similar to the one leading to Scheffé's method of multiple comparison. From the family of prediction intervals, an upper limit of the total absolute deviation Σ |XiT − eiT| is obtained, and the ratio of this limit to the projected total population is proposed as a measure of the relative precision of the projection. For a numerical study, Norwegian population data is used.