What percentage of parts will not meet the weight specs?Specifications for a part of a DVD player state that the part should weigh between 24 and 25 ounces. The process that produces the parts...

What percentage of parts will not meet the weight specs?

Specifications for a part of a DVD player state that the part should weigh between 24 and 25 ounces. The process that produces the parts yield a mean of 24.5 ounces and a standard deviation of .2 ounce. The distribution of output is normal.

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Specifications for a part of a DVD player state that the part should weigh between 24 and 25 ounces. The process that produces the parts yield a mean of 24.5 ounces and a standard deviation of .2 ounce. The distribution of output is normal.

What percentage of parts will not meet the weight specifications?

First we convert the boundary weights to z scores using `z=(x-barx)/s`

Thus for 24 oz we get z=-2.5 and for 25oz we get z=2.5.

The percentage of weights within the specifications is the area under the normal curve between z=-2.5 and z=2.5. From a table we get the area below -2.5 to be .0062, and the area below 2.5 to be .9938, so the area between them is .9938-.0062=.9876

The percentage that do not lie within the specifications is 1-.9876=.0124

So, 1.24% of the parts lie outside the specifications.

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