The efficient preparation of input distributions is an important problem in obtaining quantum advantage in a wide range of domains. We propose a novel quantum algorithm for the efficient preparation of arbitrary normal distributions in quantum registers. To the best of our knowledge, our work is the first to leverage the power of Mid-Circuit Measurement and Reuse (MCMR), in a way that is broadly applicable to a range of state-preparation problems. Specifically, our algorithm employs a repeat-until-success scheme, and only requires a constant-bounded number of repetitions in expectation. In the experiments presented, the use of MCMR enables up to a 862.6x reduction in required qubits. Furthermore, the algorithm is provably resistant to both phase-flip and bit-flip errors, leading to a first-of-its-kind empirical demonstration on real quantum hardware, the MCMR-enabled Honeywell System Models H0 and H1-2.