A filling machine is used to fill cartons with a liquid product. The specification that is strictly enforced for the machine is 9 ± 2.5 oz. If a carton produced weighs outside these bounds, it is considered by the supplier to be defective. It is hoped that at least 99% of cartons will meet these specifications. It is assumed that the weight follows a normal distribution. a. With the conditions u=9 and o=1, what proportion of cartons from the process are defective? b. If changes are made to reduce variability, what must o be reduced to in order to meet specifications with probability 0.99?

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A filling machine is used to fill cartons with a liquid product. The specification
that is strictly enforced for the machine is 9 ± 2.5 oz. If a carton produced weighs
outside these bounds, it is considered by the supplier to be defective. It is hoped that
at least 99% of cartons will meet these specifications. It is assumed that the weight
follows a normal distribution.
a. With the conditions µ=9 and o=1, what proportion of cartons from the process
are defective?
b. If changes are made to reduce variability, what must o be reduced to in order to
meet specifications with probability 0.99?
Transcribed Image Text:A filling machine is used to fill cartons with a liquid product. The specification that is strictly enforced for the machine is 9 ± 2.5 oz. If a carton produced weighs outside these bounds, it is considered by the supplier to be defective. It is hoped that at least 99% of cartons will meet these specifications. It is assumed that the weight follows a normal distribution. a. With the conditions µ=9 and o=1, what proportion of cartons from the process are defective? b. If changes are made to reduce variability, what must o be reduced to in order to meet specifications with probability 0.99?
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