Gebhardt ElectronicsGebhardt Electronics produces a wide variety of transformers that it sells directly tomanufacturers of electronics equipment. For one component used in several models of itstransformers, Gebhardt uses a 3-foot length of .20 mm diameter solid wire made of pureOxygen-Free Electronic (OFE) copper. A flaw in the wire reduces its conductivity andincreases the likelihood it will break, and this critical component is difficult to reach andrepair after a transformer has been constructed. Therefore, Gebhardt wants to use primarilyflawless lengths of wire in making this component. The company is willing to accept nomore than a l in 20 chance that a 3-foot length taken from a spool will be flawless. Gebhardtalso occasionally uses smaller pieces of the same wire in the manufacture of other compo-nents, so the 3-foot segments to be used for this component are essentially taken randomlyfrom a long spool of .20 mm diameter solid OFE copper wire.Gebhardt is now considering a new supplier for copper wire. This supplier claims that itsspools of .20 mm diameter solid OFE copper wire average 50 inches between flaws. Gebhardtnow must determine whether the new supply will be satisfactory if the supplier's claim is valid.Managerial ReportIn making this assessment for Gebhardt Electronics, consider the following three questions:1. If the new supplier does provide spools of .20 mm solid OFE copper wire that aver-age 50 inches between flaws, how is the length of wire between two consecutiveflaws distributed?2. Using the probability distribution you identified in (1), what is the probability thatGebhardt's criteria will be met (i.e., a l in 20 chance that a randomly selected 3-footsegment of wire provided by the new supplier will be flawless)?3. In inches, what is the minimum mean length between consecutive flaws that wouldresult in satisfaction of Gebhardt's criteria?4. In inches, what is the minimum mean length between consecutive flaws that wouldresult in a 1 in 100 chance that a randomly selected 3-foot segment of wire providedby the new supplier will be flawless?

For the new wire, probability of a flaw is 1/50 i.e. one flaw every 50 inch wire. If we randomly…

Geb. Gebhardt Electronics produces a wide variety of transformers that it sells directly to manufacturers of electronics equipment. For one component used in several models of its transformers, Gebhardt uses a 3-foot length of .20 mm diameter solid wire made of pure Oxygen-Free Electronic (OFE) copper. A flaw in the wire reduces its conductivity and increases the likelihood it will break, and this critical component is difficult to reach and repair after a transformer has been constructed. Therefore, Gebhardt wants to use primarily flawless lengths of wire in making this component. The company is willing to accept no more than a 1 in 20 chance that a 3-foot length taken from a spool will be flawless. Gebhardt also occasionally uses smaller pieces of the same wire in the manufacture of other compo- nents, so the 3-foot segments to be used for this component are essentially taken randomly Trom a long spool of .20 mm diameter solid OFE copper wire. Gebhardt is now considering a new supplier for copper wire. This supplier claims that its =pools of .20 mm diameter solid OFE copper wire average 50 inches between flaws. Gebhardt now must determine whether the new supply will be satisfactory if the supplier's claim is valid. Managerial Report a making this assessment for Gebhardt Electronics, consider the following three questions: 1. If the new supplier does provide spools of .20 mm solid OFE copper wire that aver- age 50 inches between flaws, how is the length of wire between two consecutive flaws distributed? 2. Using the probability distribution you identified in (1), what is the probability that Gebhardt's criteria will be met (i.e., a l in 20 chance that a randomly selected 3-foot segment of wire provided by the new supplier will be flawless)? 3. In inches, what is the minimum mean length between consecutive flaws that would result in satisfaction of Gebhardt's criteria? 4. In inches, what is the minimum mean length between consecutive flaws that would result in a 1 in 100 chance that a randomly selected 3-foot segment of wire provided by the new supplier will be flawless?

Geb. Gebhardt Electronics produces a wide variety of transformers that it sells directly to manufacturers of electronics equipment. For one component used in several models of its transformers, Gebhardt uses a 3-foot length of .20 mm diameter solid wire made of pure Oxygen-Free Electronic (OFE) copper. A flaw in the wire reduces its conductivity and increases the likelihood it will break, and this critical component is difficult to reach and repair after a transformer has been constructed. Therefore, Gebhardt wants to use primarily flawless lengths of wire in making this component. The company is willing to accept no more than a 1 in 20 chance that a 3-foot length taken from a spool will be flawless. Gebhardt also occasionally uses smaller pieces of the same wire in the manufacture of other compo- nents, so the 3-foot segments to be used for this component are essentially taken randomly Trom a long spool of .20 mm diameter solid OFE copper wire. Gebhardt is now considering a new supplier for copper wire. This supplier claims that its =pools of .20 mm diameter solid OFE copper wire average 50 inches between flaws. Gebhardt now must determine whether the new supply will be satisfactory if the supplier's claim is valid. Managerial Report a making this assessment for Gebhardt Electronics, consider the following three questions: 1. If the new supplier does provide spools of .20 mm solid OFE copper wire that aver- age 50 inches between flaws, how is the length of wire between two consecutive flaws distributed? 2. Using the probability distribution you identified in (1), what is the probability that Gebhardt's criteria will be met (i.e., a l in 20 chance that a randomly selected 3-foot segment of wire provided by the new supplier will be flawless)? 3. In inches, what is the minimum mean length between consecutive flaws that would result in satisfaction of Gebhardt's criteria? 4. In inches, what is the minimum mean length between consecutive flaws that would result in a 1 in 100 chance that a randomly selected 3-foot segment of wire provided by the new supplier will be flawless?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 32EQ

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