A tool-and-die machine shop produces extremely high-tolerance spindles. The spin

Question

A tool-and-die machine shop produces extremely high-tolerance spindles. The spindles are 18-inch slender rods used in a variety of military equipment. A piece of equipment used in the manufacture of the spindles malfunctions on occasion and places a single gouge somewhere on the spindle. However, if a defective spindle can be cut so that it has 14 consecutive inches without a gouge, then it can be salvaged for other purposes. Assume that the location of the gouge along a defective spindle is random, i.e., the distance of the location of the gouge from one end of the spindle is uniformly distributed over the interval (0, 18). If a defective spindle is randomly selected, what is the probability that it cannot be salvaged?

Explanation / Answer

P(a defective spindle can't be salvaged) = 1 - P(a defective spindle can be salvaged)

For a spindle to be salvaged, then the gouge should be present within 4 inches from either end.

So, probability that the gouge is present within 4 inches from either end = (2*4)/Total length = (2*4)/18 = 0.44

Thus,

P(a defective spindle can be salvaged) = 0.44

So,

P(a defective spindle can't be salvaged) = 1-0.44 = 0.56

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