SOLUTION: The line width for semiconductor manufacturing is assumed to be normal distributed with a mean of 0.5 micrometer and a standard deviation of 0.05 micrometer. a. What is the prob

Question 1050443: The line width for semiconductor manufacturing is assumed to be normal
distributed with a mean of 0.5 micrometer and a standard deviation of 0.05
micrometer.
a. What is the probability that a line width is greater than 0.64 micrometer?
b. What is the probability that a line width is between 0.47 and 0.65 micrometer?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
a) P(X > 0.64) = 1 - P(X < 0.64)
:
z-score = (0.64 - 0.5) / 0.05 = 2.8
:
consult z-tables for associated probability
:
P(X < 0.64) = 0.9974
:
*********************************
P(X > 0.64) = 1 - 0.9974 = 0.0026
*********************************
:
b) P(X > 0.47 and X < 0.65) = P(X<0.65) - P(X < 0.47)
:
z-score = (0.65 - 0.5) / 0.05 = 3
:
z-score = (0.47 - 0.5) / 0.05 = -0.6
:
***************************************************
P(X > 0.47 and X < 0.65) = 0.9987 - 0.2743 = 0.7244
***************************************************
:

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