The production manager at Sunny Soda, Inc., is interested in tracking the quality of the company's $12-$ounce bottle filing line. The bottles must be filled within the tolerances set for this product because the dietary information on the label shows $12$ ounces as the serving size. The design standard for the product calls for a fill level of $12\mathrm{.}00+-0\mathrm{.}10$ ounces. The manager collected the following sample data $($in fluid ounces per bottle$)$ on the production process:

$\backslash$table$[[$Sample$,$Observation$],[1,2,3,4],[1,12\mathrm{.}00,11\mathrm{.}97,12\mathrm{.}10,12\mathrm{.}08],[2,11\mathrm{.}91,11\mathrm{.}94,12\mathrm{.}10,11\mathrm{.}96],[3,11\mathrm{.}89,12\mathrm{.}02,11\mathrm{.}97,11\mathrm{.}99],[4,12\mathrm{.}10,12\mathrm{.}09,12\mathrm{.}05,11\mathrm{.}95],[5,12\mathrm{.}08,11\mathrm{.}92,12\mathrm{.}12,12\mathrm{.}05],[6,11\mathrm{.}94,11\mathrm{.}98,12\mathrm{.}06,12\mathrm{.}08],[7,12\mathrm{.}09,12\mathrm{.}00,12\mathrm{.}00,12\mathrm{.}03],[8,12\mathrm{.}01,12\mathrm{.}04,11\mathrm{.}99,11\mathrm{.}95],[9,12\mathrm{.}00,11\mathrm{.}96,11\mathrm{.}97,12\mathrm{.}03],[10,11\mathrm{.}92,11\mathrm{.}94,12\mathrm{.}09,12\mathrm{.}00],[11,11\mathrm{.}91,11\mathrm{.}99,12\mathrm{.}05,12\mathrm{.}10],[12,12\mathrm{.}01,12\mathrm{.}00,12\mathrm{.}06,11\mathrm{.}97],[13,11\mathrm{.}98,11\mathrm{.}99,12\mathrm{.}06,12\mathrm{.}03],[14,12\mathrm{.}02,12\mathrm{.}00,12\mathrm{.}05,11\mathrm{.}95],[15,12\mathrm{.}00,12\mathrm{.}05,12\mathrm{.}01,11\mathrm{.}97]]$

a$.$ Are the process average and range in statistical control?

b$.$ Is the process capable of meeting the design standard at four$-$sigma quality? Explain.