Problem $13-11($Static$)$

The following table contains the measurements of the key length dimension from a fuel injector. These samples of size five were taken at one$-$hour Intervals. Use three$-$sigma control IImits. Use Exhibit $13\mathrm{.}7.$

$\backslash$table$[[,$OBSERVATIONS$],[$SAMPLE NUMBER,$1,2,3,4,5],[1,0\mathrm{.}486,0\mathrm{.}499,0\mathrm{.}493,0\mathrm{.}511,0\mathrm{.}481],[2,0\mathrm{.}499,0\mathrm{.}506,0\mathrm{.}516,0\mathrm{.}494,0\mathrm{.}529],[3,0\mathrm{.}496,0\mathrm{.}50,0\mathrm{.}515,0\mathrm{.}488,0\mathrm{.}521],[4,0\mathrm{.}495,0\mathrm{.}506,0\mathrm{.}483,0\mathrm{.}487,0\mathrm{.}489],[5,0\mathrm{.}472,0\mathrm{.}502,0\mathrm{.}526,0\mathrm{.}469,0\mathrm{.}481],[6,0\mathrm{.}473,0\mathrm{.}495,0\mathrm{.}507,0\mathrm{.}493,0\mathrm{.}506],[7,0\mathrm{.}495,0\mathrm{.}512,0\mathrm{.}490,0\mathrm{.}471,0\mathrm{.}504],[8,0\mathrm{.}525,0\mathrm{.}501,0\mathrm{.}498,0\mathrm{.}474,0\mathrm{.}485],[9,0\mathrm{.}497,0\mathrm{.}501,0\mathrm{.}517,0\mathrm{.}506,0\mathrm{.}516],[10,0\mathrm{.}495,0\mathrm{.}505,0\mathrm{.}516,0\mathrm{.}511,0\mathrm{.}497],[11,0\mathrm{.}495,0\mathrm{.}482,0\mathrm{.}468,0\mathrm{.}492,0\mathrm{.}492],[12,0\mathrm{.}483,0\mathrm{.}459,0\mathrm{.}526,0\mathrm{.}506,0\mathrm{.}522],[13,0\mathrm{.}521,0\mathrm{.}512,0\mathrm{.}493,0\mathrm{.}525,0\mathrm{.}510],[14,0\mathrm{.}487,0\mathrm{.}521,0\mathrm{.}507,0\mathrm{.}501,0\mathrm{.}500],[15,0\mathrm{.}493,0\mathrm{.}516,0\mathrm{.}499,0\mathrm{.}511,0\mathrm{.}513],[16,0\mathrm{.}473,0\mathrm{.}506,0\mathrm{.}479,0\mathrm{.}480,0\mathrm{.}523],[17,0\mathrm{.}477,0\mathrm{.}485,0\mathrm{.}513,0\mathrm{.}484,0\mathrm{.}496],[18,0\mathrm{.}515,0\mathrm{.}493,0\mathrm{.}493,0\mathrm{.}485,0\mathrm{.}475],[19,0\mathrm{.}511,0\mathrm{.}536,0\mathrm{.}486,0\mathrm{.}497,0\mathrm{.}491],[20,0\mathrm{.}509,0\mathrm{.}490,0\mathrm{.}470,0\mathrm{.}504,0\mathrm{.}512]]$

a$.$ Calculate the mean and range for the above samples.

Note: Do not round Intermedlate calculations. Round your answers to $3$ decimal places.