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...

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.