dard deviation is $0\mathrm{.}013$ inch.

What is the process capability index?

What is the process capability ratio?

If the firm is seeking four$-$sigma performance, is the process capable of producing the bottle?

Marodin Brothers, Inc., is conducting a study to assess the capability of its $150-$gram bar soap production line. A critical quality measure is the weight of the soap bars after stamping. The lower and upper specification limits are $162$ and $170$ grams, respectively. As a part of an initial capability study, $25$ samples of size $5$ were collected by the quality assurance group and the observations in Table $3\mathrm{.}7$ were recorded.

After analyzing the data by using statistical control charts, the quality assurance group calculated the process capability ratio, and the process capability index, It then decided to improve the stamping process, especially the feeder mechanism. After making all the changes that were deemed necessary, $18$ additional samples were collected. The summary data FOR these samples are