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 components, so the 3-foot segments to be used for this component are essentially taken randomly from 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 spools 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
In 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 average 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 1 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?