We consider a system with randomly layered ferromagnetic bonds (McCoy-Wu model) and study its critical properties in the frame of mean-field theory. In the low-temperature phase there is an average spontaneous magnetization in the system, which vanishes as a power law at the critical point with the critical exponents and in the bulk and at the surface of the system, respectively. The singularity of the specific heat is characterized by an exponent . The samples reduced critical temperature has a power law distribution and we show that the difference between the values of the critical exponents in the pure and in the random system is just . Above the critical temperature the thermodynamic quantities behave analytically, thus the system does not exhibit Griffiths singularities.