The machine shop in a manufacturing plant makes three gears that fit together to become part of the gear shift mechanism for a forklift.Each part must be a specific diameter within specific tolerances.The three parts, when put together to slip into the gearbox, must also meet an overall diameter within a specific tolerance. "Nominal" is the intended or target diameter of the part. "Tolerance" is the amount of variation that is considered acceptable. For example, Part 1 should have a diameter of 1.750 inches, but the part will be considered acceptable if its diameter is as small as 1.708 inches or as large as 1.792 inches. See Table 1 below.

Part	Nominal (Target) Diameter (inches)	Tolerance (inches)
1	1.75	+0.042
2	2.00	+0.060
3	1.25	+0.030

Table 1 - Specifications

The machine shop manufactures hundreds of parts each day. The production manager randomly pulled 25 of each part from the production line to verify whether the parts are being made within the tolerance limits. Sample diameter data for the three parts are shown in Table 2 below. You may click on the link below to retrieve an EXCEL file containing the data.

https://docs.google.com/spreadsheets/d/1vCguFw9RwsvmnFcE5q-I4V4ZIrl2YsmRyzb-f3dF7T8/edit#gid=1251530720

Answer the following questions:

1. Assume the data is normally distributed. Calculate the Upper Control Limit (UCL) and Lower Control Limit (LCL) for Parts 1, 2, and 3. You may use a calculator.
2. Based on the sample data and your calculations, will the production process permit an acceptable fit of Part1at least 99.73 % of the time? Explain.
3. Will the production process permit an acceptable fit of Part 2 at least 99.73 % of the time? Explain.
4. Will the production process permit an acceptable fit of Part 3 at least 99.73 % of the time? Explain.
5. Will the production process permit an acceptable fit of all three parts combined with a specification of 5+0.081 inches at least 99.73% of the time? Note that 5 is the sum of the specifications of Parts 1, 2, and 3 while 0.081 is the sum of the tolerances for Part 1, Part 2, and Part 3.

You must show your work and explain your reasoning to get credit for Questions

Helpful hint for Question 5(all three parts together);

Collective Mean = sum of Means for Part1, Part 2, and Part 3

Collective 1 standard deviation = square root of sum of squares of individual standard deviations.

Collective UCL = (collective 1-standard deviation X 3) + collective Mean

Collective LCL = (collective 1-standard deviation X 3) - collective Mean

8. As the manager of this machine shop, would you try to decrease the variation in the manufacturing of Parts 1, 2, or 3, or is the current variation acceptable? Explain your reasoning.