Soil acidity is measured by a quantity called the ph, which may range from 0 to 14 for soils ranging from extreme alkalinity to extreme acidity. many soils have an average ph in the more-or-less- neutral 5 to 8 range. a scientist wants to estimate the average ph for a large field from n randomly selected core samples, measuring the ph of each sample. from experience he expects the standard deviation of the measurements to be 0.5. 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 of the true average ph for the field.