Calculate the probability that the sample mean of a variable falls in some range.

At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken What is the probability that the sample mean will be below 0.95 centimeters?

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We have 12 random variables here: X1, X2,... X12 (the 12 observations). These 12 observations are independent random variables: observing a number does not affect the probability distribution of the
subsequent observations (because the sample is a random sample). The sample mean is then another random variable which is obtained by summing the values of X1 through X12 and dividing them by 12:

Mean = (X1+X2+...+X12)/12

We now use ...

Solution Summary

The solution discusses at a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken What is the probability that the sample mean will be below 0.95 centimeters?

Please see attached files.
"Salaries" and instruction below.
Large Sample Case
Select the Tools pull-down menu
Choose Data Analysis
When Data Analysis dialog box appears:
Choose z-Test:Two Sample for Means
Click Ok
When the z-Test: Two Sample for Means dialog box appears:
Enter B1:B115 in theVariable 1 Range box

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1.
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