Question: Consider the clearance, C, between a shaft and a bearing. The shafts are mass produced such that the outside diameters, \(\mathrm{S}\), are normally and independently distributed with mean \(\mu_{\mathrm{s}}=1.05\) inches, and a standard deviation \(\sigma_{\mathrm{s}} .\) The bearings are produced such that the inside diameters, B, are normally and independently distributed with mean \(\mu_{\mathrm{b}}=\) 1.06 inches and a standard deviation \(\sigma_{b}=0.001\) inch. If production of shafts is to be controlled so that no more than \(1 \%\) of randomly mated shafts and bearings will exhibit interference, what is the maximum allowable value of \(\sigma_{s} ?\) Note that \(\mathrm{C}=\mathrm{B}-\mathrm{S}\).

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