Real world example

Question

Let’s say you own a company that makes bolts that are used on the International Space Station! These bolts have very specific requirements but two of the most important requirements are strength and heat resistance. NASA says that you must have a bolt that has the strength of at least X and a heat resistance of at least Y.

But when you make a bolt, there is no way you can make a bolt that equals X and Y all the time; there are just two many factors that go on in the manufacture of a bolt. So what you are looking for are bolts that are at least X or better and at least Y or better. Hence, an inequality. You can only use bolts that are in the correct range for X AND the correct range for Y.

 

But, of course, to test the bolts, you have to expose them to the extremes of both to see how they measure up. So how can you prove to NASA that your bolts will stand up? As an added problem, you never want to use bolts that you tested because that testing may have made them weaker in the process.

There is an area of Math that is used in the business world all the time to answer this type of question? Does anyone know what this area is called?

Answer 1

That field is known as statistical inference.  It entails deducing properties of a population by examining a sample of the population, with the population being much larger than the sample.  This naturally assumes the particular objects from the population that are selected for examination are indeed representative of the larger population.  In the case of bolts, you would randomly select a sample of bolts for mechanical and thermal testing, analyze the data, come up with conclusions, and assume the conclusions are valid for the entire population of bolts.  You can see some obvious questions here, like how big must the sample be.  I suggest doing some background reading in statistical inference.