The bulk density of soil is defined as the mass of dry solidsper unit bulk volume. A high bulk density implies a compact soilwith few pores. Bulk density is an important factor in influencingroot development, seedling emergence, and aeration. Let X denotethe bulk density of Pima clay loam. Studies show that X is normallydistributed with µ = 1.5 and σ = 0.2g/cm3.
(a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability.
(b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than 0.9g/ cm3.
(c) Would you be surprisedif a randomly selected sample of this type of soil has a bulkdensity in excess of 2.0g/ cm3? Explain, based on theprobability of this occurring.(d) What point has the propertythat only 10% of the soil samples have bulk density this high orhigher?
(e) What is the momentgenerating function for X?