Final answer:
The resulting LCL for developing a three-sigma R-chart with an average range of 14 and a sample size of 6 is 7.55.
Step-by-step explanation:
To develop a three-sigma R-chart, you need to calculate the lower control limit (LCL). The LCL is given by the formula LCL = avg range - (3 x avg range / d2), where d2 is a constant depending on the sample size. In this case, the sample size is 6, so the constant d2 is 2.059. Plugging in the values, LCL = 14 - (3 x 14 / 2.059) = 14 - 6.45 = 7.55.