Question

1. A production process is designed to fill boxes with an average of 14 ounces of cereal. The population of filling weights is normally distributed with a standard deviation of 3 ounces.

a. Calculate the centerline, the upper control limit (UCL), and the lower control limit (LCL) for the x¯x¯ chart if samples of 12 boxes are taken. (Round the value for the centerline to the nearest whole number and the values for the UCL and LCL to 3 decimal places.)

b. Analysts obtain the following sample means after a recent inspection of the production process. Can they conclude that the process is under control?

x¯1=14.7x¯1=14.7	x¯2=14.7x¯2=14.7	x¯3=13.3x¯3=13.3	x¯4=13.5x¯4=13.5	x¯5=13.5x¯5=13.5	x¯6=13.1x¯6=13.1

• Yes because all sample means lie within the control limits and there is no systematic pattern.
• Yes because some sample means lie outside the control limits.
• No because some sample means lie outside the control limits.
• No because even though all sample means lie within the control limits there is a negative trend.

Answer 1