A memory system may include a memory device and a memory controller. The memory device may include memory cells. The memory controller may estimate and use an read voltage to distinguish one or more memory cells corresponding to a first threshold voltage distribution from one or more memory cells corresponding to a second threshold voltage distribution, the read voltage being estimated based on standard deviations and average threshold voltages of the first and the second threshold voltage distributions and probability density functions corresponding to the first and the second threshold voltage distributions, respectively. The memory controller may be structured and operable to calculate the standard deviation of the first threshold voltage distribution, based on a first probability area distinguished by a first target read voltage, a second probability area distinguished by a second target read voltage, and inverse Q-function values corresponding to the first and the second probability areas.