Core i5 and i7 are two different types of CPU manufactured byIntel. As you may know as a matter of fact, Intel does not producetwo types of CPUs. Instead, they just produce Core i7 chips.However, since a chip contains many millions of transistors, someof the transistors may not work properly, while other regions fromthe chip are working perfectly. In this case, Intel does not scrapthe chip to trash, as it will be a waste, but deactivates themalfunctioning region and sell it as a cheaper chip, named Core i5,with less but perfectly functional features. Suppose an assemblyline is able to manufacture 3000 chips per day. The probabilitythat a chip meets the Core i7 standard is independently 1/1000.(While the background of this question is real, the probabilityhere is much lower than the true probability.) An assembly line isqualified if it is able to produce at least 3 Core i7 per day. (a)Write down the exact expression of the probability that thisassembly line is qualified if it operates only one day. (b) Writedown a relevant approximate expression for the probability from(a).
Consider the assembly line described in the above question.Since Core i7 makes much more profit than Core i5, Intel decides tomanufacture more chips in a day in order to produce sufficient Corei7 chips per day with high probability. Specifically, the CEO wantsto get at least 3 Core i7 chips per day with probability at least0.999. How many assembly lines should Intel purchase in total?
