Discuss the below in detail:
Q: A quality control inspector at Cocoa Fizz is using the data from above to develop control limits. If the average range for the twenty-five samples is .29 ounces (computed as 7.17/25) and the average mean of the observations is 15.95 ounces, develop three-sigma control limits for the bottling operation without knowing the standard deviation of the population.
|
Observations
|
|
|
|
|
Sample
|
(bottle volume in ounces)
|
Average
|
Range
|
|
Number
|
1
|
2
|
3
|
4
|
|
R
|
|
1
|
15.85
|
16.02
|
15.83
|
15.93
|
15.91
|
0.19
|
|
2
|
16.12
|
16.00
|
15.85
|
16.01
|
15.99
|
0.27
|
|
3
|
16.00
|
15.91
|
15.94
|
15.83
|
15.92
|
0.17
|
|
4
|
16.20
|
15.85
|
15.74
|
15.93
|
15.93
|
0.46
|
|
5
|
15.74
|
15.86
|
16.21
|
16.10
|
15.98
|
0.47
|
|
6
|
15.94
|
16.01
|
16.14
|
16.03
|
16.03
|
0.20
|
|
7
|
15.75
|
16.21
|
16.01
|
15.86
|
15.96
|
0.46
|
|
8
|
15.82
|
15.94
|
16.02
|
15.94
|
15.93
|
0.20
|
|
9
|
16.04
|
15.98
|
15.83
|
15.98
|
15.96
|
0.21
|
|
10
|
15.64
|
15.86
|
15.94
|
15.89
|
15.83
|
0.30
|
|
11
|
16.11
|
16.00
|
16.01
|
15.82
|
15.99
|
0.29
|
|
12
|
15.72
|
15.85
|
16.12
|
16.15
|
15.96
|
0.43
|
|
13
|
15.85
|
15.76
|
15.74
|
15.98
|
15.83
|
0.24
|
|
14
|
15.73
|
15.84
|
15.96
|
16.10
|
15.91
|
0.37
|
|
15
|
16.20
|
16.01
|
16.10
|
15.89
|
16.05
|
0.31
|
|
16
|
16.12
|
16.08
|
15.83
|
15.94
|
15.99
|
0.29
|
|
17
|
16.01
|
15.93
|
15.81
|
15.68
|
15.86
|
0.33
|
|
18
|
15.78
|
16.04
|
16.11
|
16.12
|
16.01
|
0.34
|
|
19
|
15.84
|
15.92
|
16.05
|
16.12
|
15.98
|
0.28
|
|
20
|
15.92
|
16.09
|
16.12
|
15.93
|
16.02
|
0.20
|
|
21
|
16.11
|
16.02
|
16.00
|
15.88
|
16.00
|
0.23
|
|
22
|
15.98
|
15.82
|
15.89
|
15.89
|
15.90
|
0.16
|
|
23
|
16.05
|
15.73
|
15.73
|
15.93
|
15.86
|
0.32
|
|
24
|
16.01
|
16.01
|
15.89
|
15.86
|
15.94
|
0.15
|
|
25
|
16.08
|
15.78
|
15.92
|
15.98
|
15.94
|
0.30
|
|
Total
|
|
|
|
|
398.75
|
7.17
|