8.18 Suppose that X1, …, and Y1, …, constitute independent random samples from populations with means and and variances and , respectively. Then the Central Limit Theorem can be extended to show that is approximately normally distributed for large n1 and n2, with mean (m1 - m2) and variance

(o/n)+(/m). Water flow through soils depends, among other things, on the porosity (volume proportion due to voids) of the soil. To compare two types of sandy soil, n = 50 mea- surements are to be taken on the porosity of soil A, and n = 100 measurements are to be taken on soil B. Assume that a 0.01 and o=0.02. Find the approximate probability that the differ- ence between the sample means will be within 0.05 unit of the true difference between the pop- ulation means, (-2).