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.

Bicycle Parts Co.
Sample Means and Standard Deviations
Part 1		Part 2		Part 3
1.74831		2.01144		1.25426
1.75740		2.00448		1.24775
1.75134		2.01492		1.24558
1.73316		2.00448		1.24992
1.75134		2.00448		1.23907
1.71498		2.00100		1.25860
1.75437		2.00796		1.25643
1.73619		2.00100		1.25209
1.73922		1.98708		1.25426
1.73619		1.99752		1.24341
1.74528		1.99752		1.25643
1.74831		2.00100		1.24775
1.76346		1.99404		1.24341
1.74528		2.00796		1.24558
1.76952		2.00448		1.23907
1.70892		2.00448		1.24124
1.75134		2.00100		1.24558
1.71195		1.99752		1.24992
1.74831		2.00100		1.25209
1.77861		2.00100		1.24992
1.75740		1.98708		1.24992
1.73619		1.99404		1.24558
1.74225		1.98708		1.24992
1.74528		1.98360		1.24775
1.73922		2.00100		1.24775

1. 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?