A vegetable packing company wants to facilitate packaging of carrots by sorting them into groups of relatively uniform length and diameter. The company decides to evaluate sorting by means of a weight sizing machine. It wants to determine whether it can sort on the basis of weight or whether it must measure both the weight and the length (major diameter) of the carrots. As a part of their feasibility study, they decide to evaluate several samples of carrots arriving at their packing facility a. For purposes of the study (not for routine sorting), what instruments/apparatus could they use to measure the dimensions and volume of the carrots? b. How could the company determine whether there is a relationship between: (1) weight and length; and (2) length (major diameter) and the "intermediate diameter"? (Note: the intermediate diameter will be taken as the average of the maximum and minimum diameters measured at the thickest cross section which is perpendicular to the major diameter.) c. What criteria could be used to evaluate the "reliability" of the use of weight for predicting size?