  This paper theoretically analyzes a phenomenological stochastic model for
bacterial growth. This model comprises cell division and the linear growth of
cells, where growth rates and cell cycles are drawn from lognormal
distributions. We find that the cell size is expressed as a sum of independent
lognormal variables. We show numerically that the quality of the lognormal
approximation greatly depends on the distributions of the growth rate and cell
cycle. Furthermore, we show that actual parameters of the growth rate and cell
cycle take values that give a good lognormal approximation; thus, the
experimental cell-size distribution is in good agreement with a lognormal
distribution.
