A manufacturer has been working to implement a just$-$in$-$time inventory system for its

production line. The final product requires the installation of a pneumatic tube at a particular

station.

Ideally, the tubes would arrive just as the operator needed them, but the company expects a

buildup of an average of $20$ tubes.

The supervisor does not want the inventory variance of tubes to be greater than $16.$

On a given day, the buildup at the workstation is determined at eight different times, and the

following values are recorded:

$2317202921141924$

What would be the appropriate decision considering $=0\mathrm{.}05?$