Suppose a lling machine is used to ll cartons with a liquid product. The specica

Question

Suppose a lling machine is used to ll cartons with a liquid product. The specication that is strictly enforced for the lling machine is 9 ± 1.5 oz. If any carton is produced with weight outside these bounds, it is considered by the supplier to be defective. It is hoped that at least 99% of cartons will meet these specications. With the conditions = 9 and = 1, what proportion of cartons from the process are defective? If changes are made to reduce variability, what must be reduced to in order to meet specications with probability 0.99? Assume a normal distribution for the weight.

Explanation / Answer

1)proportion of cartons from the process are defective =P(7.5<X<10.5) =P((7.5-9)/1<Z<(10.5-9)/1)

=P(-1.5<Z<1.5)=0.9332-0.0668 =0.8664

2) for 99% of cartons to meet these specications ; z score =2.5758

therefore std deviation =margin of error /z =1.5/2.5758=0.5823

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