Question

[10 points] For a shaft-bearing assembly, the shaft diameters were found to have an average of 2.1 in., with a standard deviation of 0.12 in. The bearing bore diameters were found to have an average of 2.2 in., with a standard deviation of 0.07 in. What proportion of the assemblies will have a clearance of less than 0.01 in.? Assume that the shaft and bearing dimensions are independent

Answer 1

Let shaft diameters be denoted as X and bearing bore diameters be denoted as Y.

Assumption : X ~ N( _X ,_X²) Y ~ N(_Y ,_Y²)

Y - X ~ N( _Y - _X , _X² + _Y²)

Given :   _X = 2.1 in , _X = 0.12 in , _Y = 2.2 in , _Y = 0.07 in

Required Probability

[We get the above probability from the Standard Normal table]

Thus 26% of the assemblies will have a clearance of less than 0.01 in.