8.48 Soil acidity is measured by a quantity called pH. A scientist wants to estimate the difference in the average pH for two large fields using pH measurements from randomly selected core samples. If the scientist selects 20 core samples from field I and 15 core samples from field 2, independently of each other, find the approximate probability that the sample mean of the 40 pH measurements for field 1 will be larger than that for field 2 by at least 0.5.The sample variances for pH measurements for fields I and II are 1 and 0.8, respectively. In the past, both fields have shown approximately the same mean soil acidity levels.