We calculate the inclusive branching ratio for B-->X(s)gamma the inclusive branching ratios and asymmetries for B-->X(s)l(+)l(-), and the anomalous magnetic moment g(mu)-2 of the muon, within a minimal gauge-mediated supersymmetry-breaking model which naturally generates a large ratio tan beta of Higgs field vacuum expectation values. These predictions are highly correlated with each other, depending on only two fundamental parameters: the superpartner mass scale and the logarithm of a common messenger mass. The predictions for B -->X(s)gamma decay and g(mu)-2 are in somewhat better agreement with current experiments than the standard model, but a much sharper comparison will soon be possible using new measurements now in progress or under analysis. Moreover we predict large deviations in B-->X(s)e(+)e(-) and B-->X(s)mu(+)mu(-) asymmetries, and somewhat smaller ones in B-->X(s)e(+)e(-) and B-->X(s)tau(+)tau(-) branching ratios, which will be detectable in hadronic colliders. [S0556-2821(98)00521-9].