2. For 127 consecutive days, a process engineer has measured the temperature of champagne bottles as they are made ready for serving. Each day, she took a sample of 5 bottles. The average across all 635 bottles (127 days, 5 bottles per day) was 43 degrees Fahrenheit. The standard deviation across all bottles was 1.0 degrees Fahrenheit.

When constructing an X-bar chart, what would be the upper control limit?

Note: Round your intermediate calculations and final answer to 4 decimal places.

10. A grinding process has an upper specification of 1.318 millimeters and a lower specification of 1.216 millimeters. A sample of parts had a mean of 1.28 millimeters with a standard deviation of 0.028 millimeters.

What standard deviation will be needed to achieve a process capability index of 2.0?

Note: Round your answer to 5 decimal places.

11. In the welding operations of a bicycle manufacturer, a bike frame has a flow time of about 14.5 hours. The time in the welding operation is spent as follows: 1 hour waiting in front of the cutting machine for the batch to start, 2 hours waiting for the setup of the machine, 2 hours waiting for the other pieces of the batch to go through cutting, 1 minute at the cutting machine, and 3 hours waiting for the transfer to the welding machine. Then, at the welding machine, the unit spends 2 hours waiting in front of the welding machine for the batch to start, 2 hours waiting for the setup of the welding machine, 0.5 hours waiting for the other pieces of the batch to go through welding, 0.75 minutes at the welding machine, and 2 hours waiting for the transfer to the next department.

Determine the exact flow time. What is the value-added percentage of the flow time?

Note: Round your percentage answer to 4 decimal places.

12. A sample of 19 parts is weighed every hour. After 38 hours, the standard deviation of the data is 0.18 grams. You wish to prepare an X-bar chart of this data.

What is the estimated standard deviation (ESD) of this data?

Note: Round your answer to 4 decimal places.