The minimum breaking strength for a $0\mathrm{.}50$ Wire$-$Core Elevator Wire Rope is $8000$lbs$.$ This wire$-$rope is supplied in large lots, and a variable sampling plan is to be used to sentence the lots.$$

It is desired by both the customer and the supplier to have

$=0\mathrm{.}10,$p$=$AQL$=0\mathrm{.}02$

$=0\mathrm{.}05.$p$=$LTPD$=0\mathrm{.}10$

The variability of the wire$-$rope is unknown but will be estimated by the sample standard deviation.

$($a$)$Find an appropriate one$-$sided variable sampling plan $($Form $1)$ according to the above risk requirements.$$

$($b$)$Suppose that a sample of the appropriate size $($as calculated in $($a$))$ was taken from a specific lot, and we got $=9300\mathrm{.}0,$ s$=500.$ Should the lot be accepted or rejected based on the Form $1$ criteria?