InGreen Supplies produces a wide variety of equipment that it sells directly to manufacturers of cannabis-derived products. For one component used in several models of its extraction systems,   InGreen uses a 3-foot length of .20 mm diameter coil (solid wire made of copper). A flaw in the wire reduces the active recovery and increases the likelihood it will break, and this critical component is difficult to reach and repair after the system has been assembled.   InGreen has position itself as the industry mos reliable supplier and, consequently, it wants to use primarily flawless lengths of wire in making this component. The company is willing to accept n more than a 1 in 15 chance that a 3-foot length taken from a spool will be flawless.   InGreen 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 copper   wire.  InGreen is now considering a new supplier for copper wire. This supplier claims that its spools of .20 mm diameter solid copper wire average 50 inches between flaws.   InGreen now must determine whether the new supply will be satisfactory if the supplier's claim is valid.

 Deliverable

You must write a report to assess whether the new supply will be satisfactory.  In your analysis, you must consider the following three questions:

1. If the new supplier does provide spools of .20 mm solid copper wire that average 50 inches between flaws, how is the length of wire between two consecutive flaws distributed?
2. Using the probability the distribution you identified in (1), what is the probability that InGreen'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 result in the satisfaction of InGreen's criteria?
4. In inches, what is the minimum mean length between consecutive flaws result in a 1 in 100 chance that a randomly selected 3-foot segment of wire provided by the new supplier will be flawless?.