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40. The bulk density of soil is defined as the mass of dry solids per unit bulk vol- ume. A high bulk density implies a compact soil with few pores. Bulk density is an important factor in influencing root development, seedling emergence, and aeration. Let X denote the bulk density of Pima clay loam. Studies show that X is normally distributed with u = 1.5 and o = .2 g/cm3. (a) What is the density for X? Sketch a graph of the density function. Indicate on this graph the probability that X lies between 1.1 and 1.9. Find this probability. (b) Find the probability that a randomly selected sample of Pima clay loam will have bulk density less than .9 g/cm3. (c) Would you be surprised if a randomly selected sample of this type of soil has a bulk density in excess of 2.0 g/cm3? Explain, based on the probabil- ity of this occurring. (d) What point has the property that only 10% of the soil samples have bulk density this high or higher? oldermy mob Isunion's 21 (e) What is the moment generating function for X? all s