You\'re in charge of an operation that manufactures steel dowels with a specific
ID: 381626 • Letter: Y
Question
You're in charge of an operation that manufactures steel dowels with a specification of 100 mm +/- 1 mm in length. You're concerned about the quality in your process and have taken the following samples. What is the probability of exceeding the maximum dimension?
Sample
Measurement
1
100.15
2
99.85
3
99.75
4
99.15
5
100.25
6
101.05
7
98.9
8
100.15
9
100.05
10
99.95
11
98.85
12
100.5
13
100.75
14
100.65
15
99.75
16
100.05
17
99.25
18
101.15
19
98.95
20
99.95
21
100.15
22
100
23
100.15
24
99.95
25
101.05
Sample
Measurement
1
100.15
2
99.85
3
99.75
4
99.15
5
100.25
6
101.05
7
98.9
8
100.15
9
100.05
10
99.95
11
98.85
12
100.5
13
100.75
14
100.65
15
99.75
16
100.05
17
99.25
18
101.15
19
98.95
20
99.95
21
100.15
22
100
23
100.15
24
99.95
25
101.05
Explanation / Answer
We place all the values of measurement in excel and derive following values for process mean ( m ) and Sample standard deviation ( Sd ) using formula AVG ( ) and STDDEV.S ( )
Accordingly ,
Process mean = m = 100.016
Sample standard deviation = Sd = 0.632
Maximum dimension = 100 + 1 = 101 mm
Probability of exceeding maximum dimension of 101 mm
= 1 – Probability of process outcome to be maximum 101 mm
Let Z value corresponding to probability that maximum dimension to be 101 mm is Z1
Accordingly,
M + Z1.Sd = 101
Or , 100.016 + 0.632.Z1 = 101
Or, Z1 = 1.55 ( ROUNDED TO 2 DECIMAL PLACES )
Corresponding value of probability for Z1 = 1.55 ( from standard normal distribution table ) will be 0.93943
Therefore ,
Probability that maximum dimension will exceed 101 mm = 1 - 0.93943 = 0.06057
PROBABILITY OF EXCEEDING MAXIMUM DIMENSION = 0.06057
PROBABILITY OF EXCEEDING MAXIMUM DIMENSION = 0.06057
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