I have the below question in my book, and I\'ve calculated the probability the c
ID: 3149712 • Letter: I
Question
I have the below question in my book, and I've calculated the probability the capacitor falls within the specified +- .5 micron range as .3829 or 38.29%, but how do I calculate the last part of the question. "The group wants a 98% chance that any order of capacitors would contain the sufficient number of usable items." What's confusing is the 98% chance it falls within the range (or 2% chance of falling out of the range). 2,090 units should yield 100% within the range, but that's not what the question asks. Any thoughts on how to solve this?
Chad Williams, field geologist for the American Oil Company, settled into his first class seat on the Sun-Air flight between Los Angeles and Oakland, California. Earlier that afternoon, he had attended a meeting with the design engineering group at the Los Angeles New Product Division. He was now on his way to the home office in Oakland. He was looking forward to the one hour flight because it would give him a chance to reflect on a problem that surfaced during the meeting. It would also give him a chance to think about the exciting opportunities that lay ahead in Australia. 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.
Explanation / Answer
The language of question formulation is quite controversial. At the best it can be considered that if in 98% cases 800 capacitors are functioning then its ok. So the number of capacitors that you have calculated , if there are 0.98 proportion of capacitor then also its ok. Thus the number of capacitor should be 0.98*2090 or approximately 2048 capacitors.