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?

The solution is very helpful to understand the concept of these ...

Solution Summary

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.

... In recent year, scores on a standardized test for high ... is more than 2275 hours because the z-score is within ... Use the standard normal table to find the z-score...

... But the table is just for a standard normal distribution ... So, for a general normal distribution X~ N ( µ , σ 2 ... we need to convert values a to z-score as follows ...

... X as normal with mean µ = 100*0.73 = 73 and standard deviation σ = 100 ... Standardizing the variable X using X − 73 Z score and from normal distribution we ...

...Normal Probabilities. Common Data Mean 7.55 Standard Deviation 1.86. Probability for X > X Value 5.62 Z Value -1.037634409 P(X>5.62) 0.8503. Page 1 Normal3. ...

... the calculation of probability using the Z score. ... a short description on Standard normal distribution. Probabilities, z scores and distributions 1. Two hundred ...

... b. Find the z-score for each score in the population. ... a mean of μ = 60 and a standard deviation of ... of the following probabilities for a normal distribution ...

... the details of calculation of probability, Z scores and percentiles ... souvenirs, is $130 with a standard deviation of $12 ... Assume that this distribution is normal. ...

... the lower 25% of standarized scores from the ... that is find the z-score corresponding to P25 ... The percentages of the standard normal distributions are determined ...

... Cumulative Percentage 75.00% Z Value 0.67448975 X Value 567.448975. 3. A normal distribution has a mean of µ = 80 and a standard deviation of σ = 10. ...