8.8 The soil acidity is measured by a quantity called pH, which may range from 0 to 14 for soils ranging from low to high acidity. Many soils have an average pH in the 5–8 range. A scientist wants to estimate the average pH for a large field from n randomly selected core samples by measuring the pH in each sample. If the scientist selects n  40 samples, find the approximate probability that the sample mean of the 40 pH measurements will be within 0.2 unit of the true average pH for the field.