# Approximate normal distribution.

Problem 1: A machine is producing metal pieces that are cylindrical in shape. A sample of pieces is taken and the diameters are 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03 cm. Find a 99% confidence interval of the true mean diameter of pieces from this machine, assuming an approximate normal distribution.
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user_27qwe

$n=9,\stackrel{―}{x}=1.0056,s=0.0245,{t}_{0.005}=3.355$ with 8 degrees of freedom.

$1.0056-\left(3.355\right)\left(0.0245/3\right)<\mu <1.0056+\left(3.355\right)\left(0.0245/3\right)$

$0.978<\mu <1.033$