A restaurant is improving its processes, and is currently focusing on the final bill presented to customers. The manager samples $50$ bills per day for $12$ days, and checks to see how many are incorrect using a z$-$value of $3.$

$[$ Select $]["$Special cause is evident since day $6$ is above UCL", $"$No special cause is evident", "Special cause is evident since $5$ different days are above and $7$ are below average complaint rates", "Special cause is evident since the Upper Control Limit is above the z$-$value of $3"]$ Is the billing process consistent $($in other words, is it in control$),$ or do special cause events appear to be present?

$[$ Select $]["14\mathrm{.}56$ incorrect bills", $"\mathrm{.}1456$ incorrect bills", $"\mathrm{.}1456\%","14\mathrm{.}56\%"]$ What is the UCL?

$[$ Select $]["3\mathrm{.}13\%",$ "There is no LCL since there is always at least $1$ incorrect bill in the sample", $"0\%","5\mathrm{.}17\%"]$ What is the LCL$?$

Day Day $1$ Day $2$ Day $3$ Day $4$ Day $5$ Day $6$ Day $7$ Day $8$ Day $9$ Day $10$ Day $11$ Day $12$

Incorrect Bills $132148211314$

You collect two more days of data, again sampling $50$ bills per day, and add the results $(11$ incorrect bills on day $13,$ and $9$ on day $14)$ to the control chart.

$[$ Select $]["3","2","0","1"]$ How many days are now outside the control limits$?$

$[$ Select $]["\mathrm{.}1879\%","14\mathrm{.}56\%","18\mathrm{.}31\%","\mathrm{.}1456\%"]$ What is the UCL?

$[$ Select $]["$There is no LCL since there is always at least $1$ incorrect bill in the sample", $"5\mathrm{.}17\%","7\mathrm{.}58\%","0\%"]$ What is the LCL$?$