The machine shop in a bicycle manufacturing firm makes three gears that fit together to become part of the gear shift mechanism for the bicycle. Each part must be a specific diameter within specific tolerances. The three parts, when put together to slip into the rear wheel of the bike, must also meet an overall diameter within a specific tolerance.
Samples for the three parts were taken.
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Bicycle Parts Co.
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Sample Means and Standard Deviations
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Part 1
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Part 2
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Part 3
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1.74831
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2.01144
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1.25426
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1.75740
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2.00448
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1.24775
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1.75134
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2.01492
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1.24558
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1.73316
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2.00448
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1.24992
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1.75134
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2.00448
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1.23907
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1.71498
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2.00100
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1.25860
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1.75437
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2.00796
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1.25643
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1.73619
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2.00100
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1.25209
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1.73922
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1.98708
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1.25426
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1.73619
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1.99752
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1.24341
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1.74528
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1.99752
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1.25643
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1.74831
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2.00100
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1.24775
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1.76346
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1.99404
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1.24341
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1.74528
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2.00796
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1.24558
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1.76952
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2.00448
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1.23907
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1.70892
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2.00448
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1.24124
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1.75134
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2.00100
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1.24558
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1.71195
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1.99752
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1.24992
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1.74831
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2.00100
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1.25209
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1.77861
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2.00100
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1.24992
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1.75740
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1.98708
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1.24992
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1.73619
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1.99404
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1.24558
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1.74225
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1.98708
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1.24992
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1.74528
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1.98360
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1.24775
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1.73922
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2.00100
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1.24775
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- Calculate the mean and standard deviations for each part and compare them to the following specification limits:
Part Nominal (inches) Tolerance (inches)
1 1.750 + 0.045
2 2.000 + 0.060
3 1.250 + 0.030
2. Will the production process permit an acceptable fit of Part 1 at least 99.73 percent of the time?
3. Will the production process permit an acceptable fit of Part 2 at least 99.73 percent of the time?
4. Will the production process permit an acceptable fit of Part 3 at least 99.73 percent of the time?
5. Will the production process permit an acceptable fit of all three part combined into a slot with a specification of 5 + 0.081 inches at least 99.73% of the time?