Mining Engineering (October 2004) published a study of a new technology for producing high-quality iron nuggets directly from raw iron ore and coal. For one phase of the study, the percentage change in the carbon content of the produced nuggets was measured at 4-hour intervals for 33 consecutive intervals. The data for the 33 time intervals are listed in the table below. Specifications state that the carbon content should be within 3.42 ± 0.3 percent.

a. Construct a capability analysis diagram for the iron making process.
b. Determine the proportion of carbon measurements that fall outside specifications.
c. Find the capability index for the process and interpret its value.

Carbon Carbon Change (%) Interval Change (%) Interval 3.25 18 3,55 3.30 19 3.48 3 3.23 20 3.42 3.40 3.00 21 3.51 22 3.50 6. 3.60 23 3.45 3.75 3.52 3.65 24 3.50 8. 25 3.40 26 3.10 3.25 3.78 10 3.35 27 3.48 3.50 11 28 12 29 3.70 13 3.25 3.60 3.55 30 3.50 14 31 3.40 15 32 3.45 16 3.60 33 3.30 17 2.90