This letter presents a detailed investigation of the random telegraph noise (RTN) effects on the threshold-voltage distribution of flash memory arrays programmed by the staircase algorithm. RTN is shown to introduce an exponential tail above the program verify level when considering the cell threshold voltage that ends the program operation. In addition, when a subsequent read operation is considered, a clear exponential tail is shown to appear even below the program verify level. We present a simple analysis that is able to predict the threshold-voltage distribution width accounting for both these enlargement contributions, defining practical formulas for the programming accuracy as a function of the staircase step amplitude and the RTN distribution.