Question

Construct a pivot table (frequency table) of the data from Manufacturing Example xlsx

What is the probability that a randomly selected piece is out of spec?

Round to 2 decimals (ie, 0.04)

Inspection Data L1

1.062

1.066

1.066

1.060

1.066

1.066

1.060

1.059

1.067

1.064

1.066

1.063

1.06

1.06

1.067

1.065

1.059

1.066

1.07

1.063

1.062

1.071

1.061

1.061

1.071

1.066

1.063

1.070

1.069

1.059

1.059

1.067

1.063

1.062

1.07

1.061

1.070

1.069

1.071

Answer 1

From the given data, we get the following table:

x	Frequency	P(X=x)	x*P(X=x)	x2*P(X=x)
1.059	4	0.102564	0.108615	0.115024
1.06	4	0.102564	0.108718	0.115241
1.061	3	0.076923	0.081615	0.086594
1.062	3	0.076923	0.081692	0.086757
1.063	4	0.102564	0.109026	0.115894
1.064	1	0.025641	0.027282	0.029028
1.065	1	0.025641	0.027308	0.029083
1.066	7	0.179487	0.191333	0.203961
1.067	3	0.076923	0.082077	0.087576
1.069	2	0.051282	0.054821	0.058603
1.07	4	0.102564	0.109744	0.117426
1.071	3	0.076923	0.082385	0.088234
Total	39	1	1.064615	1.133421

The probability is calculated as: frequency\total frequency
The mean is calculated as:


Also,

The variance is calculated as:






It is known that,
the specification limit is given by (under 3 - sigma limits):

Now the required probability is,

None of the randomly selected sample will out of specification limit.

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