In experiments we always observe a definite outcome in an individual experiment. The question: In which sense is this compatible with the wave nature of quantum mechanics? is called the quantum measurement problem. It has been discussed many times, mostly at a philosophical level. par We introduce and solve a realistic Hamiltonian model for a quantum measurement within standard quantum statistical mechanics. The model describes the measurement of the z-component of a spin through interaction with a magnetic memory. The latter apparatus is modeled by a Curie - Weiss magnet having $Ngg 1$ spins weakly coupled to a phonon bath. par The solution of the dynamics is very rich, but finally yields exactly the properties summarized in the collapse postulate and Born rule. The irreversibility of the measurement is ensured by the large size of the apparatus. Nothing else than the usual quantum statistical mechanics and Schrödinger equation is needed, and the results support a specific version of the statistical interpretation. In this light, other interpretations appear as non-minimal. par For the measurement problem the model offers a physical way out of the mathematical embarrassment. par This talk summarizes the review: Armen E. Allahverdyan, Roger Balian and Theo M. Nieuwenhuizen, Understanding quantum measurement from the solution of dynamical models, arXiv:1003.0453v2 (201 pages, 375 references, Physics Reports, in press). Here we advocate the statistical interpretation for teaching.