We present a search for the standard model Higgs boson production in association with a W boson in proton-anti proton collisions (pp arrow right W super(+ or -)H arrow right lnubb) at a center of mass energy of 1.96 TeV. The search employs data collected with the CDF II detector which correspond to an integrated luminosity of approximately 2.7 fb super(-1). We recorded this data with two kinds of triggers. The first kind required high-p sub()Tcharged leptons and the second required both missing transverse energy and jets. The search selects events consistent with a signature of a single lepton (e super(+ or -)/ mu super(+ or -)), missing transverse energy, and two jets. Jets corresponding to bottom quarks are identified with a secondary vertex tagging method and a jet probability tagging method. Kinematic information is fed in an artificial neural network to improve discrimination between signal and background. The search finds that both the observed number of events and the neural network output distributions are consistent with the standard model background expectations, and sets 95% confidence level upper limits on the production cross section times branching ratio. The limits are expressed as a ratio to the standard model production rate. The limits range from 3.6 (4.3 expected) to 61.1 (43.2 expected) for Higgs masses from 100 to 150 GeV /c super(2), respectively.