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Problem 33

Suppose that diameters of a shaft s manufactured by a certain machine are normal random variables with mean 10 and s.d. \(0.1 .\) If for a given application the shaft must meet the requirement that its diameter falls between \(9.9\) and \(10.2 \mathrm{~cm}\). What proportion of shafts made by this machine will meet the requirement?

Expert verified

The proportion of shafts produced by this machine that will meet the requirement is 0.8185

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Chapter 2

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$$
f_{X}(x)=\left\\{\begin{array}{ll}
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