This dissertation describes a search for the Standard Model Higgs boson produced in association with the Z boson via Higgs-strahlung at the CDF II detector at the Tevatron. At a Higgs boson mass between 100 GeV/c2 and 135 GeV/c2, the primary Higgs decay mode is to a pair of b quarks. The associated Z boson can decay to a pair of electrons or muons, allowing detection of a final event signature of two visible leptons and two b quarks. This final state allows reduction of large QCD backgrounds compared to a hadronic Z boson decay, leading to a more sensitive search. To increase sensitivity, standard model matrix element probabilities for ZH signal and the dominant backgrounds are used as components to a likelihood fit in signal fraction. In 2.7 fb−1 of CDF II data, we see no evidence of production of a Higgs boson with a mass between 100 GeV c2 and 150 GeV/c2. Using the Feldman-Cousins technique to set a limit, at 95% coverage and a Higgs boson mass of 115 GeV/c2, the median expected limit was 12.1 x [sigma]{sub SM} and a limit of 8.2 x [sigma]{sub SM} was observed, where [sigma]{sub SM} is the NNLO theoretical cross section of p{bar p} →ZH → l +l -b{bar b} at √s=1.96 TeV . Cross section limits are computed at a range of Higgs boson mass values between 100 GeV/c 2 and 150 GeV/c2.