Answer to Question #264814 in Statistics and Probability for ron

Question

The line width for semiconductor manufacturing is assumed to be normally distributed with a mean of 0.5 micrometer and a standard deviation of 0.05 micrometer. What is the probability that a line width is greater than 0.62 micrometer?

Answer 1

Mean = 0.5

Standard deviation = 0.05

$P(X>0.62)=1-(Z>\frac{X-\mu}{\sigma})$

$P(X>0.62)=1-(Z>\frac{0.62-0.50}{0.05})=1-(Z>2.4)$

From Z normal distribution table, p-value is:

$P(X>0.62)=1-0.9918=0.0082$

This means there is only 0.82% of the probability that a line width is greater than 0.62 micrometer.