  We point out that in theories where the gravitino mass, $M_{3/2}$, is in the
range (10-50)TeV, with soft-breaking scalar masses and trilinear couplings of
the same order, there exists a robust region of parameter space where the
conditions for electroweak symmetry breaking (EWSB) are satisfied without large
imposed cancellations. Compactified string/M-theory with stabilized moduli that
satisfy cosmological constraints generically require a gravitino mass greater
than about 30 TeV and provide the natural explanation for this phenomenon. We
find that even though scalar masses and trilinear couplings (and the
soft-breaking $B$ parameter) are of order (10-50)TeV, the Higgs vev takes its
expected value and the $\mu$ parameter is naturally of order a TeV. The
mechanism provides a natural solution to the cosmological moduli and gravitino
problems with EWSB.
