One of the greatest challenges for neutrino experimentation is understanding the potential uncertainties in the collected data and models that are used for the Monte Carlo simulations. The neutrino-nucleus hadronic cross sections are a direct input to the determination of the flux in any accelerator neutrino beam. The high intensity of the NuMI beamline (Neutrinos at the Main Injector) at Fermilab, in Batavia, IL, allows us to study neutrino oscillations and neutrino interactions with high statistics. The uncertainties on the knowledge of the flux is associated with the production and attenuation of hadrons in the beamline materials and with the beam optics. The EMPHATIC collaboration is developing a hadron production experiment that will be used to constrain flux uncertainties in order to reduce them significantly. The group has taken data impinging 20GeV/c, 30GeV/c and 120GeV/c energy protons into thick (> 1 interaction length) carbon targets during the EMPHATIC beam test in January 2018. The analysis of the new data provides great details on hadron production cross-section. This thesis will highlight specific details within the standard model and its association with neutrino properties. It will also highlight some particle accelerator physics with applications of Monte Carlo simulations, including the current NuMI beam simulation and the uncertainty estimates using PPFX software. It also provides an overview of the EMPHATIC experiment and its engineering test run made in January, 2018. Lastly, by implementing the improved measurements on the 120 GeV proton impinging on a carbon target data that was collected by the latest EMPHATIC test run, data will show verification of a strong improvement for the neutrino flux uncertainty used among several experiments.