The sensitivity of the Compact Muon Solenoid (CMS) detector at the Large Hadron Collider (LHC) for 95% confidence limit exclusion, 3σ significant observation, and 5σ significant discovery of the Standard Model (SM) Higgs Boson in the H → ZZ* → 4μ decay channel is studied using Monte Carlo tools. The results are in terms of the median probability of achieving a statistically significant result as a function of integrated luminosity. Monte Carlo simulated Higgs boson signal samples from 115–200 GeV along with the ZZ, tt¯ and Zbb¯ background samples were generated assuming[special characters omitted] = 10 TeV proton collision energy, and subject to full detector simulation and reconstruction. The Geometrical Discriminator (GD) cut is developed for finding the size of the intersection radius for 4 charged tracks by minimizing the "spatial variance" formed by points on each of the tracks and compared with other prospective experimental methods (cuts). GD is shown to perform with better efficiency in rejecting background events and accepting signal events when compared with impact parameter based cuts (SIP3D). A sequence of m_H independent cuts is developed to derive a 4μ sample from the bulk of the signal and background MC data. Optimized m_H dependent GD cuts are then used over the events passing the cuts at each mass point and the probability calculations are performed. The calculated median integrated luminosities required to set 95% CL exclusion limits for m_H = 115 and 120 GeV are 130.3 and 54.1 fb⁻¹ respectively. Median integrated luminosities of 8.3, 6.0, 4.6 and 4.0 are required to make a 95% CL exclusion limit on m_H = 140, 150, 190, and 200 GeV respectively. 3σ significant observation requires a median integrated luminosity of 6.9, 5.0, 6.0 and 5.7 fb⁻¹ for the m_H = 140, 150, 190 and 200 GeV mass points respectively.