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# Standard Normal Distribution

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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?

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#### 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.

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