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

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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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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?

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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 ...

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