The Log-normal Distribution. In atmospheric science, the Log-normal distribution is often used to characterize particle size distributions. In one study, the distribution of silicone nanoparticle size (in nm) was found to be approximately Log-normal with Log-mean = 3.91 and Log-sd w = 0.47. Suppose the desired range of particle sizes is (40nm, 110nm). What percentage of silicone nanoparticles do you expect to fall within this range?