Final answer:
The six sigma range for a production process with an average diameter of 3 inches and a standard deviation of 1/200 of an inch is from 2.97 inches to 3.03 inches.
Step-by-step explanation:
The question is asking for the six sigma range of a production process that creates gaskets. The six sigma range is a statistical measure that is used in quality control. It represents the range within which 99.99966% of all manufactured gaskets should fall if the process is operating correctly.
This range is calculated as the mean plus or minus six times the standard deviation. Given an average diameter of 3 inches and a standard deviation of 1/200 of an inch, we use the formula mean ± 6(standard deviation) to calculate the six sigma range.
- Six sigma lower bound = mean - 6 × (standard deviation) = 3 - 6 × (1/200) = 3 - 0.03 = 2.97 inches
- Six sigma upper bound = mean + 6 × (standard deviation) = 3 + 6 × (1/200) = 3 + 0.03 = 3.03 inches
Therefore, the six sigma range of this production process is from 2.97 inches to 3.03 inches.