An article in Journal of Hydrology [“Use of a Lognormal Distribution Model for Estimating Soil Water Retention Curves from Particle-Size Distribution Data” (2006, Vol. 323(1), pp. 325–334)] considered a lognormal distribution model to estimate water retention curves for a range of soil textures. The particle-size distribution (in centimeters) was modeled as a lognormal random variable X with θ = −3.8 and ω = 0.7. Determine the following:

(a) P(X < 0.02)

(b) Value for x such that P(X ≤ x) = 0.95

(c) Mean and variance of X