  We report the first observation of the baryonic flavor-changing neutral
current decay Lambda_b -> Lambda mu+ mu- with 24 signal events and a
statistical significance of 5.8 Gaussian standard deviations. This measurement
uses ppbar collisions data sample corresponding to 6.8fb-1 at sqrt{s}=1.96TeV
collected by the CDF II detector at the Tevatron collider. The total and
differential branching ratios for Lambda_b -> Lambda mu+ mu- are measured. We
find B(Lambda_b -> Lambda mu+ mu-) = [1.73+-0.42(stat)+-0.55(syst)] x 10^{-6}.
We also report the first measurement of the differential branching ratio of B_s
-> phi mu+ mu- using 49 signal events. In addition, we report branching ratios
for B+ -> K+ mu+ mu-, B0 -> K0 mu+ mu-, and B -> K*(892) mu+ mu- decays.
