# Standard Normal Distribution

The diameter of a shaft in an optical storage drive is normally distributed with mean 0.2508 inch and standard deviation 0.0005inch. The specifications of the shaft are 0.2500+/-0.0015 inch.

a.) What proportion of the shafts conforms to specifications?

b.) What can be done to reduce non-conforming proportion?

Â© BrainMass Inc. brainmass.com March 4, 2021, 5:58 pm ad1c9bdddfhttps://brainmass.com/statistics/normal-distribution/proportion-shaft-optical-storage-drive-21343

#### Solution Preview

a)

<br>Specifications of the shaft diameter D are 0.2500+/-0.0015 inch.

<br>

<br>Hence (0.2500 + 0.0015) > D > (0.2500 - 0.0015

<br>that is, 0.2515 > D > 0.2485 ... these are the upper and lower limits allowed.

<br>

<br>Now find the ...

#### Solution Summary

The solution determines what proportion of the shafts conforms to specifications and what can be done to reduce non-conforming proportion.

$2.49