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The photoresist thickness in semiconductor
Chapter 5, Problem 71E(choose chapter or problem)
Problem 71E
The photoresist thickness in semiconductor manufacturing
has a mean of 10 micrometers and a standard deviation of
1 micrometer. Assume that the thickness is normally distributed
and that the thicknesses of different wafers are independent.
(a) Determine the probability that the average thickness of 10
wafers is either greater than 11 or less than 9 micrometers.
(b) Determine the number of wafers that need to be measured
such that the probability that the average thickness exceeds
11 micrometers is 0.01.
(c) If the mean thickness is 10 micrometers, what should the
standard deviation of thickness equal so that the probability
that the average of 10 wafers is either more than 11 or less
than 9 micrometers is 0.001?
Questions & Answers
QUESTION:
Problem 71E
The photoresist thickness in semiconductor manufacturing
has a mean of 10 micrometers and a standard deviation of
1 micrometer. Assume that the thickness is normally distributed
and that the thicknesses of different wafers are independent.
(a) Determine the probability that the average thickness of 10
wafers is either greater than 11 or less than 9 micrometers.
(b) Determine the number of wafers that need to be measured
such that the probability that the average thickness exceeds
11 micrometers is 0.01.
(c) If the mean thickness is 10 micrometers, what should the
standard deviation of thickness equal so that the probability
that the average of 10 wafers is either more than 11 or less
than 9 micrometers is 0.001?
ANSWER:
Solution :
Step 1 of 3:
Given that the thickness in semiconductor (X) manufacturing has mean is 10 micrometers, and standard deviation is 1 micrometer.
Our goal is:
a). We need to find the probability of thickness of 10 wafer is either greater than 11 or less than 9.
b). We need to find the number of wafers that need to be measured.
c). We need to find the standard deviation of thickness.
a). We assume that the thickness is normally distributed and thickness of 10 wafer is either greater than 11 or less than 9 micrometer.
We know that standard deviation is 1 and the sample size n is 10.
Now we need to find the sample standard deviation.
Then the sample standard deviation formula is
The probability of thickness of 10 wafer is either greater than 11 or less than 9 is
P(
Then,
From the table value,.
Hence the required probability is
P(
P(
P(
Therefore, the probability of thickness of 10 wafer is either greater than 11 or less than 9 is 0.0016.