Solution Found!
Consider the semiconductor wafer data in Table 2-1.
Chapter 3, Problem 153E(choose chapter or problem)
Consider the semiconductor wafer data in Table 2-1. Suppose that 10 wafers are selected randomly (without replacement) for an electrical test. Determine the following:
(a) Probability that exactly 4 wafers have high contamination.
(b) Probability that at least 1 is from the center of the sputtering tool and has high contamination.
(c) Probability that exactly 3 have high contamination or are from the edge of the sputtering tool.
(d) Instead of 10 wafers, what is the minimum number of wafers that need to be selected so that the probability that at least 1 wafer has high contamination is greater than or equal to 0.9?
Questions & Answers
QUESTION:
Consider the semiconductor wafer data in Table 2-1. Suppose that 10 wafers are selected randomly (without replacement) for an electrical test. Determine the following:
(a) Probability that exactly 4 wafers have high contamination.
(b) Probability that at least 1 is from the center of the sputtering tool and has high contamination.
(c) Probability that exactly 3 have high contamination or are from the edge of the sputtering tool.
(d) Instead of 10 wafers, what is the minimum number of wafers that need to be selected so that the probability that at least 1 wafer has high contamination is greater than or equal to 0.9?
ANSWER:
Solution
Step 1 of 4
a) We have to find the probability of exactly 4 wafers have high contamination
Given that 10 wafers are selected at random
Then N=582+358=940
k=358
n=10
x=4
The pmf of hypergeometric distribution is
Now we have to find
=0.2502
Hence the probability of exactly 4 wafers have high contamination is 0.2502