Question

4. Core i5 and i7 are two different types of CPU manufactured by Intel. As you may know as a matter of fact, Intel does not produce two types of CPUs. Instead, they just produce Core i7 chips. However, since a chip contains many millions of transistors, some of the transistors may not work properly, while other regions from the chip are working perfectly. In this case, Intel does not scrap the chip to trash, as it will be a waste, but deactivates the malfunctioning region and sell it as a cheaper chip, named Core i5, with less but perfectly functional features. Suppose an assembly line is able to manufacture 3000 chips per day. The probability that a chip meets the Core i7 standard is independently 1/1000. (While the background of this question is real, the probability here is much lower than the true probability.) An assembly line is qualified if it is able to produce at least 3 Core i7 per day. a) Write down the exact expression of the probability that this assembly line is qualified if it operates only one day. (b) Write down a relevant approximate expression for the probability from (a).

5. Consider the assembly line described in the above question. Since Core i7 makes much more profit than Core i5, Intel decides to manufacture more chips in a day in order to produce sufficient Core i7 chips per day with high probability. Specifically, the CEO wants to get at least 3 Core i7 chips per day with probability at least 0.999. How many assembly lines should Intel purchase in total? (You might need wolframalpha.com or other devices to solve an equation.)

Answer 1

Solution:-

(a)

An assembly line is able to manufacture 3000 cgips per day

so, n = 3000

The probability that a chip meets the core i7 standard is

so, p =

Let x be the number of good chip

,

An assembly line is qualified if

= 1 - (.4231) = 0.5769

So, probability is 0.5769 if we assembles line need to quality.

(b)

To find approximate estimate on the probability we need to approximate distribution. since p is very less, n is bir, np = 3 (finite small number) so, we can say

now,

  

= 1 - .4232 = .5768

Both the probabilities are almost same.

X1 = number of qualified chip from 1st assembly line

X2 = number of qualified chip from 2nd assembly line

.....Xn = number of qualified chip from nth assembly line

we assume that n assembly lines are required

y is sum of n independent poisson

for n = 2

for n = 3

for n = 4

> .999

So, n = 4

so, 4 assembly lines are required.