# Team Project 1: Normal Distribution: American Oil Company Case Study Narrative: American Oil is a company that uses advanced equipment to detect oil…

American Oil is a company that uses advanced equipment to detect oil under the earth’s surface. Chad Williams is a field geologist who has recently learned that a design-engineering group in the company has come up with an enhancement to their current equipment that will greatly improve their ability to detect and find oil. However, this enhancement requires the use of 800 electrical capacitors. These capacitors must operate within +/- 0.5 microns from the standard of

12 microns. Chad knows therefore that not all capacitors will meet the specifications required by the new equipment. So in order to have at least 800 useable capacitors, American Oil will have to order more than 800 from the supplier. However, since these items are very expensive, he wants to order as few as possible to meet their needs. The group agreed that they want at least a 98% chance that any order of capacitors would contain a sufficient number of useable items. Chad is wondering if a statistical technique can be used to help determine how many capacitors to order.

Case Study Student Hints:

The main question is: What is the probability of any one capacitor having a mean between 11.5 and 12.5 when the population mean is 12 with a standard deviation of 1

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