# Standard Normal or Z score for finding the probability

Yashchin (1995) discusses a process for the chemical etching of sillicon wafer used in integrated circuits. This process etches the layer of silicon dioxide until the layer of mental beneath is reached. This company moniters the thickness of the silicon oxide layer because thicker layers require longer etching times. Historically, the layer has a true mean thickness of 1 micron and a standard deviation of 0.06 micron.

a. A recent random sample of four wafers yielded a sample mean of 1.134. Find the probability of observing such a mean of something smaller assuming the historic mean and standard deviation.

b. What did you assume in order to find this probability?

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This solution is comprised of a detailed explanation of standard normal distribution or z score. In this solution, step-by-step explanation of this complicated topic provides students with a clear perspective of standard normal distribution to find the probability.