Discuss the below:
1) Twenty five items were selected at random a production process and their quality characteristic was measured resulting in the following data:
|
i
|
x
|
|
i
|
x
|
|
1
|
97.00
|
|
16
|
78.82
|
|
2
|
87.22
|
|
17
|
94.32
|
|
3
|
102.44
|
|
18
|
95.96
|
|
4
|
112.76
|
|
19
|
101.35
|
|
5
|
111.98
|
|
20
|
96.35
|
|
6
|
121.33
|
|
21
|
96.73
|
|
7
|
78.16
|
|
22
|
96.30
|
|
8
|
97.66
|
|
23
|
113.43
|
|
9
|
110.95
|
|
24
|
99.15
|
|
10
|
89.13
|
|
25
|
98.14
|
|
11
|
93.10
|
|
|
|
|
12
|
83.10
|
|
|
|
|
13
|
81.53
|
|
|
|
|
14
|
90.22
|
|
|
|
|
15
|
92.26
|
|
|
|
The spec limits are set at 80 and 120.
Estimate the proportion of the production that will not meet spec. Show your approach, rationale, analysis, and results.
2) In addition, each of the 25 items selected were inspected to determine the number of defects per unit with the following results.
0, 2, 0, 1, 1, 2, 1, 1, 0, 0, 1, 0, 1, 1, 2, 1, 1, 0, 2, 3, 0, 1, 2, 0, 3
(a) Analyze this data and summarize your results.
(b) Estimate the probability that a randomly selected item will have at least 3 defects.