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 $3.$

Day

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$11$

$12$

Incorrect Bills

$1$

$3$

$2$

$1$

$4$

$8$

$2$

$1$

$1$

$3$

$1$

$4$

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Is the billing process consistent $($in other words, is it in control$),$ or do special cause events appear to be present?

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What is the UCL?

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What is the LCL$?$

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.

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How many days are now outside the control limits$?$

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What is the UCL?

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What is the LCL$?$