A customer's specification for weight of an antiseptic cream sold in plastic tubes is between $4\mathrm{.}9$ and $5\mathrm{.}1$ ounces, i$.$e$.,5\mathrm{.}00+-0\mathrm{.}1$ ounces. At Brooklyn Pharmaceuticals, the distribution of the filling process is centered at $5\mathrm{.}02$ ounces with a standard deviation of $0\mathrm{.}04$ ounces.

$\backslash$table$[[$a$,\backslash$table$[[$Please fill the green cells $(10$ points$)],[$USL$]],2$ points each$],[],[,$LSL$,]]$

$\backslash$table$[[$ZUSL$,],[$ZISL$,],[$Sigma Capability Z$,]]$

How many standard deviation the process mean is away from the upper specification limit$?$ How many standard deviation the process mean is away from the lower specification limit$?$

b With a target sigma capability of $3,$ determine whether the process is capable? $(10$ points$)$

c If the company can successfully improve the process and have the filling process centered at exactly $5\mathrm{.}00$ ounces, can they achieve the target sigma capability of $3?(10$ points$)$

d

If the company reduces the variation in the filling process and maintains a standard deviation of $0\mathrm{.}03$ ounces $($average mean still at $5\mathrm{.}02$ ounces$),$ can they achieve the target sigma capability of $3?(10$ points$)$