Question

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 i and R charts based on these subgroups are constructed, we find that these charts are in statistical control with = 0.8267 and R = .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. (Round your answers to 4 decimal places.) The range of values = (b) Find a reasonable estimate of the maximum weight of a grapefruit that the grocer is likely to sell. (Round your answer to 4 decimal places.) Maximum weight to sell pounds (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? Note here that there is no upper specification, since we would like grapefruits to be as large as possible. (Round your answer to 4 decimal places.) No grapefruit weights might be as low as pounds.

Answer 1

Answer:

a)

Given,

Range = xbar +/- 3*(Rbar/d2)

substitute values

= 0.8267 +/- 3*0.11/1.693

= 0.8267 +/- 0.1949

= (0.6318 , 1.0216)

b)

Maximum weight = 1.0216

c)

No

Minimum weight = 0.6318

d)

Consider,

Rbar/d2 = 0.11/1.693 = 0.06497

Consider,

P(X < 0.75) = P(z < (0.75 - 0.8267)/0.06497)

= P(z < - 1.18)

= 0.1190001 [since from z table]

= 0.1190

= 11.90%