  Massive exoplanets are observed preferentially around high metallicity
([Fe/H]) stars while low-mass exoplanets do not show such an effect. This
so-called planet-metallicity correlation generally favors the idea that most
observed gas giants at $r<10$ AU are formed via a core accretion process. We
investigate the origin of this phenomenon using a semi-analystical model,
wherein the standard core accretion takes place at planet traps in protostellar
disks where rapid type I migrators are halted. We focus on the three major
exoplanetary populations - hot-Jupiters, exo-Jupiters located at $r \simeq 1$
AU, and the low-mass planets. We show using a statistical approach that the
planet-metallicity correlations are well reproduced in these models. We find
that there are specific transition metallicities with values [Fe/H]$=-0.2$ to
$-0.4$, below which the low-mass population dominates, and above which the
Jovian populations take over. The exo-Jupiters significantly exceed the
hot-Jupiter population at all observed metallicities. The low-mass planets
formed via the core accretion are insensitive to metallicity, which may account
for a large fraction of the observed super-Earths and hot-Neptunes. Finally, a
controlling factor in building massive planets is the critical mass of
planetary cores ($M_{c,crit}$) that regulates the onset of runaway gas
accretion. Assuming the current data is roughly complete at [Fe/H]$>-0.6$, our
models predict that the most likely value of the "mean" critical core mass of
Jovian planets is $\braket{M_{c,crit}} \simeq 5 M_{\oplus}$ rather than $10
M_{\oplus}$. This implies that grain opacities in accreting envelopes should
play an important role in lowering $M_{c,crit}$.
