The Stryker Baseball Bat Company manufactures wooden and aluminum baseball bats at its plant in New England. Wooden bats produced for the mass market are turned on a lathe, where a piece of wood is shaped into a bat with a handle and barrel. The bat is cut to its specied length and then nished in subsequent processes. A specic style of wooden bat is supposed to have a mean barrel circumference of 9 inches with 0.5 inches tolerance at its thickest point.

The company is trying to buy a new machine to cut the bats due to a projected increase in sales. There are three different candidate machines that the company is trying to buy at different costs. The following table summarizes the process average, process standard deviation (SD), and purchase cost of each machine. Which machine, if any, should the company purchase (they are trying to buy the cheapest machine that can get the job done)?

Machine	Average	SD	Purchase Cost
1	9.35	0.14	$20,000
2	8.93	0.16	$18,000
3	9.00	0.18	$15,000

1. Determine the Upper Specification Limit.
2. Determine the Lower Specification Limit.
3. Calculate the process capability index of machine 1.
4. Based on process capability index of machine 1, is machine 1 capable?
   1. Yes
   2. No
5. Calculate the process capability index of machine 2.
6. Based on process capability index of machine 2, is machine 2 capable?
   1. Yes
   2. No
7. Calculate the process capability index of machine 3.
8. Based on process capability index of machine 3, is machine 3 capable?
   1. Yes
   2. No
9. Which machine should the company purchase?
   1. Machine 1
   2. Machine 2
   3. Machine 3
   4. None of these