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Gouges on a spindle. A tool-and-die machine shop produces
Chapter 4, Problem 151E(choose chapter or problem)
Problem 151E
Gouges on a spindle. 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 the spindle can be cut so that it has 14 consecutive inches without a gouge, then the spindle can be salvaged for other purposes. Assuming that the location of the gouge along the spindle is random, what is the probability that a defective spindle can be salvaged?
Questions & Answers
QUESTION:
Problem 151E
Gouges on a spindle. 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 the spindle can be cut so that it has 14 consecutive inches without a gouge, then the spindle can be salvaged for other purposes. Assuming that the location of the gouge along the spindle is random, what is the probability that a defective spindle can be salvaged?
ANSWER:
Solution 151E
Step1 of 2:
Let us consider a random variable ‘X’ it presents the number of inches a gouge is from one end of the spindle. Here X follows uniform distribution with parameters also we have the spindle can be cut so that it has 14 consecutive inches without a gouge.
We need to find the probability that a defective spindle can be salvaged.