A grocer has a contract with a produce wholesaler that specifies that the wholesaler will supply the grocer with grapefruit that weigh at least .75 pounds each. In order to monitor the grapefruit weights, the grocer randomly selects three grapefruit from each of 25 different crates of grapefruit received from the wholesaler. Each grapefruit’s weight is determined and, therefore, 25 subgroups of three grapefruit weights are obtained. When x̅ and R charts based on these subgroups are constructed, we find that these charts are in statistical control with x̅̅ = .8467 and R̅ = .11. Further, a histogram of the individual grapefruit weights indicates that these measurements are approximately normally distributed.
a. Calculate a range of values that contains almost all (approximately 99.73 percent) of the individual grapefruit weights.
b. Find a reasonable estimate of the maximum weight of a grapefruit that the grocer is likely to sell.
c. Suppose that the grocer’s contract with its produce supplier specifies that grapefruits are to weigh a minimum of .75 lb. Is this lower specification being met? Explain. Note here that there is no upper specification because we would like grapefruits to be as large as possible.
d. If the lower specification of .75 lb. is not being met, estimate the fraction of grapefruits that weigh less than .75 lb.