Chad works with a small group of highly trained people at American Oil who literally walk the earth looking for new sources of oil. They make use of the latest in electronic equipment to take a wide range of measurements from many thousands of feet below the earth's surface. It is one of these electronic machines that is the source of Chad's current problem. Engineers in Los Angeles have designed a sophisticated enhancement that will greatly improve the equipment's ability to detect oil. The enhancement requires 800 capacitors, which must operate within ±0.50 microns from the specified standard of 12 microns.
The problem is that the supplier can provide capacitors that operate according to a normal distribution, with a mean of 12 microns and a standard deviation of 1 micron. Thus, Chad knows that not all capacitors will meet the specifications required by the new piece of exploration equipment. This will mean that in order to have at least 800 usable capacitors, American Oil will have to order more than 800 from the supplier. However, these items are very expensive, so he wants to order as few as possible to meet their needs. At the meeting, the group agreed that they wanted a 98% chance that any order of capacitors would contain the sufficient number of usable items. If the project is to remain on schedule, Chad must place the order by tomorrow. He wants the new equipment ready to go by the time he leaves for an exploration trip to Australia.
As Chad reclined in his seat, sipping cool lemonade, he wondered whether a basic statistical technique could be used to help determine how many capacitors to order. Could you help him and come up with the answer for him?