You work for the Quality Assurance Department of a manufacturing company. Your c
ID: 3358690 • Letter: Y
Question
You work for the Quality Assurance Department of a manufacturing company. Your company manufactures pencils. Machine A, Pencil Maker, is set to produce pencils of mean length 190mm with a standard deviation of 0.1mm. Machine B, Pencil Giant, produces pencils of mean length 190mm with a standard deviation of 0.2mm. Your boss believes that the machines are not producing pencils of correct length. As the Quality Assurance Officer, you must select a sample of pencils, measure the length of each pencil and use the data to determine whether your boss’ claim is true.
Machine A Machine B
1 190.2 190.1
2 190.0 190.2
3 190.1 190.2
4 190.2 190.2
5 190.2 190.1
6 190.2 190.3
7 190.1 190.2
8 190.0 190.4
9 190.3 190.4
10 190.3 190.4
11 190.0 190.2
12 190.0 190.0
13 190.0 190.1
14 190.2 190.4
15 190.1 190.3
16 190.1 190.5
17 190.1 190.4
18 190.4 190.0
19 190.4 190.2
20 190.3 190.4
21 190.3 190.2
22 190.2 190.1
23 190.0 189.8
24 190.3 189.7
25 190.1 190.0
26 190.3 189.5
27 189.7 189.5
28 189.8 189.9
29 189.7 189.6
30 189.9 189.7
31 189.9 189.8
32 189.7 189.9
33 189.7 189.5
34 189.9 189.7
35 189.7 189.7
36 189.8 189.7
37 189.7 189.5
38 189.9 189.8
39 189.8 189.6
40 189.6 189.7
Use a frequency table to summarize the lengths of the pencils produced by both machines.
Explanation / Answer
Following are the freqeuncy table of machine A and machine B:
For machine A, 16 pencils are within 0.1 mm of 190 mm. That is proprotion of pencils within specification is
16 /40 = 0.40
For machine B, 9 pencils are within 0.1 mm of 190 mm. That is proprotion of pencils within specification is
9 /40 = 0.225
Machine A Frequency Machine B Frequency 189.6 1 189.5 4 189.7 6 189.6 2 189.8 3 189.7 6 189.9 4 189.8 3 190 6 189.9 2 190.1 6 190 3 190.2 6 190.1 4 190.3 6 190.2 7 190.4 2 190.3 2 190.4 6 190.5 1Related Questions
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