STATISTICAL PROCESS CONTROL: Control chart question

Scenario: The manager of the customer service hotline for an internet service provider has been approached by the President of the company regarding a perceived increase in the number of customer complaints regarding the lack of timely technical assistance being provided by hotline technicians.  In order to evaluate the validity of the President’s concerns he decided to survey customers regarding their satisfaction with the timeliness of the technical assistance they received.  Surveys were conducted during a thirty-day period with two hundred (200) randomly selected customers participating in the survey each day.  The number of customers surveyed who expressed dissatisfaction with the timeliness of the technical assistance they received is summarized in the following table.

Day

No. Complaints, X

Proportion of Complaints, p = X / 200

1

22

0.110

2

29

0.145

3

25

0.125

4

17

0.085

5

20

0.100

6

16

0.080

7

31

0.155

8

16

0.080

9

31

0.155

10

29

0.145

11

15

0.075

12

12

0.060

13

22

0.110

14

23

0.115

15

27

0.135

16

15

0.075

17

17

0.085

18

17

0.085

19

19

0.095

20

22

0.110

21

23

0.115

22

27

0.135

23

29

0.145

24

41

0.205

25

21

0.105

26

24

0.120

27

22

0.110

28

24

0.120

29

23

0.115

30

31

0.155

Total

690

3.450

Question 1: Using the data contained in the scenario, calculate the Upper Control Limit for the number of complaints that reflect a 95.5% confidence level. 

Question 2: Using the data contained in the scenario, calculate the Lower Control Limit for the number of complaints that reflect a 95.5%confidence level. 

Question 3:Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for the number of complaints, which samples are out of control?

Question 4:Using the data contained in the scenario, calculate the Upper Control Limit for the proportion of complaints that reflect 95.5% level of confidence.

Question 5:  Using the data contained in the scenario, calculate the Lower Control Limit for the proportion of complaints that reflect 95.5% level of confidence.

Question 6: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for the proportion of complaints, which samples are out of control?