A certain production process produces two parts: a bearing and a shaft. In the final assembly the

Question:

A certain production process produces two parts: a bearing and a shaft. In the final assembly the shaft and bearing are randomly mated and a critical specification is the clearance between the two parts. The of the inside diameters of the bearing is normally distributed with a mean equal to 5.40 mm with a standard deviation of 0.735 mm. The of the outside diameters of the shaft is normally distributed with a mean equal to 3.93 mm with a standard deviation of 0.413 mm.
a. Estimate the mean and variance of the of clearances for the bearing-shaft assemblies.
b. Assuming that the mating of bearings and shafts is random estimate the proportion of assemblies that will not fit together. (Hint: The assemblies will not fit together if the clearance is less than or equal to zero.)
c. By how much would the variance in clearances have to be reduced so that the proportion of defective assemblies is less than 1%?
Distribution
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