Q#2)To determine if their0.50centimeter castings are properly adjusted, Clapton Industries has decided to use anx-Chart which uses the range to estimate the variability in the sample.

Step 4 of 7:Use the following sample data, taken from the next time period, to determine if the process is "In Control" or "Out of Control".

Observations:0.54, 0.55, 0.55, 0.56, 0.5, 0.57

Sample Mean:0.545

Step 5 of 7:Use the following sample data, taken from the next time period, to determine if the process is "In Control" or "Out of Control".

Observations:0.49, 0.47, 0.47, 0.48, 0.48, 0.5

Sample Mean:0.4817

Step 6 of 7:Use the following sample data, taken from the next time period, to determine if the process is "In Control" or "Out of Control".

Observations:0.53, 0.51, 0.54, 0.51, 0.46, 0.54

Sample Mean:0.515

Step 7 of 7:Based on the control limits established, what is the probability that the production manager will conclude that the process is "Out of Control", when the process is actually "In Control"? Round your answer to three decimal places.