Five data entry operators work at the data processing department of the Birmingham Bank. Each day for $30$ days, the number of defective records in a sample of $250$ records typed by these operators has been noted, as follows:

SAMPLE NO$.$ NO$.$ DEFECTIVE SAMPLE NO$.$ NO$.$ DEFECTIVE SAMPLE NO$.$ NO$.$ DEFECTIVE

$1711182117$

$251252212$

$3191316236$

$410144247$

$51115112513$

$681682610$

$71217122714$

$89184286$

$961962912$

$10132016303$

Establish

$3$

$$

upper and lower control limits$.$

Why can the lower control limit not be a negative number?

The industry standards for the upper and lower control limits are $0\mathrm{.}10$ and $0\mathrm{.}01,$ respectively. What does this imply about Birmingham Bank$$s own standards? PX

$$ S$6\mathrm{.}19$ Houston North Hospital is trying to improve its image by providing a positive experience for its patients and their relatives. Part of the $$image$$ program involves providing tasty, inviting patient meals that are also healthful. A questionnaire accompanies each meal served, asking the patient, among other things, whether he or she is satisfied or unsatisfied with the meal. A $100-$patient sample of the survey results over the past $7$ days yielded the following data:

DAY NO$.$ OF UNSATISFIED PATIENTS SAMPLE SIZE

$124100$

$222100$

$38100$

$415100$

$510100$

$626100$

$717100$

Construct a p$-$chart that plots the percentage of patients unsatisfied with their meals. Set the control limits to include $99\mathrm{.}73\%$ of the random variation in meal satisfaction. Comment on your results. PX