We report the results of magnetic, magnetocaloric properties, and critical behavior investigation of the double-layered perovskite manganite La-1.4(Sr0.95Ca0.05)(1.6)Mn2O7. The compounds exhibits a paramagnetic (PM) to ferromagnetic (FM) transition at the Curie temperature T-C = 248 K, a Neel transition at T-N = 180 K, and a spin glass behavior below 150 K. To probe the magnetic interactions responsible for the magnetic transitions, we performed a critical exponent analysis in the vicinity of the FM-PM transition range. Magnetic entropy change (-Delta S-M) was estimated from isothermal magnetization data. The critical exponents beta and gamma, determined by analyzing the Arrott plots, are found to be T-C = 248 K, beta = 0.594, gamma = 1.048, and delta = 2.764. These values for the critical exponents are close to the mean-field values. In order to estimate the spontaneous magnetization M-S(T) at a given temperature, we use a process based on the analysis, in the mean-field theory, of the magnetic entropy change (-D Delta(M)) versus the magnetization data. An excellent agreement is found between the spontaneous magnetization determined from the entropy change [(-Delta S-M) vs. M-2] and the classical extrapolation from the Arrott curves (mu H-0/M vs. M-2), thus confirming that the magnetic entropy is a valid approach to estimate the spontaneous magnetization in this system and in other compounds as well.