Core-collapse supernova explosions expose the structure and environment of massive stars at the moment of their death. We use the global fitting technique of Pejcha & Prieto (2015a,b) to estimate a set of physical parameters of 19 normal Type II SNe, such as their distance moduli, reddenings, $^{56}$Ni masses M${\rm Ni}$, and explosion energies E${\rm exp}$ from multicolor light curves and photospheric velocity curves. We confirm and characterize known correlations between MNi and bolometric luminosity at 50 days after the explosion, and between MNi and Eexp. We pay special attention to the observed distribution of M${\rm Ni}$ coming from a joint sample of 38 Type II SNe, which can be described as a skewed-Gaussian-like distribution between 0.005 M${\odot}$ and 0.280 M${\odot}$, with a median of 0.031 M${\odot}$, mean of 0.046 M${\odot}$, standard deviation of 0.048 M${\odot}$ and skewness of 3.050. We use two-sample Kolmogorov-Smirnov test and two-sample Anderson-Darling test to compare the observed distribution of MNi to results from theoretical hydrodynamical codes of core-collapse explosions with the neutrino mechanism presented in the literature. Our results show that the theoretical distributions obtained from the codes tested in this work, KEPLER and Prometheus Hot Bubble, are compatible with the observations irrespective of different pre-supernova calibrations and different maximum mass of the progenitors.