Question

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 300 records typed by these operators has been​ noted, as​ follows:
                                                                                                                     

Sample No.

No. Defectives

Sample No.

No. Defectives

Sample No.

No. Defectives

1

8

11

7

21

17

2

4

12

5

22

13

3

19

13

16

23

6

4

10

14

3

24

6

5

12

15

12

25

13

6

9

16

8

26

11

7

11

17

13

27

15

8

10

18

4

28

7

9

6

19

18

29

13

10

14

20

17

30

4

a) Establish 3σ upper and lower control limits.

​​UCLp ​= (enter your response as a number between 0 and​ 1, rounded to three decimal​ places).

LCPp =(enter your response as a number between 0 and​ 1, rounded to three decimal​ places).

b) Why can the lower limit not be a negative number? (I actually know this one but I wanna get all the points down)

c) The industry standards for the upper and lower control limits are 0.10 and 0.01, respectively. What does this imply about Birmingham Bank's own standards?

Answer 1

Answer:

Step-by-step explanation:

a)

• p = Total Number of Defects / Sample Size x Number of Samples

• 302 / 300 x 30 = 0.0336

• z = Number of standard deviation = 3

• σ = Standard deviation of sampling distribution

• σ = p (1- p) / n = 0.0336 (1- 0.0336) / 300 = 0.0336 x 0.9664 / 300 = 0.0104

• Here, n = number of observations in each sample

• UCL = p+zσ = 0.0336 + 3(0.0104) = 0.0336 + 0.0312 = 0.0648 = 0.065

• LCL = p-zσ = 0.0336 - 0.0312 = 0.0024 = 0.002

b) Hence, Lower control limit cannot be a negative number as percent defective cannot be a negative number. As such, No. Percent of defective records cannot be a negative number.