Your supervisor, Lisa Lehmann, has asked that you report on the output of a machine on the factory floor. This machine is supposed to be producing optical lenses with a mean weight of 50 grams and a range of 3.5 grams. The following table contains the data for a sample size of n = 6 taken during the past 3 hours:

SAMPLE NUMBER 1 2 3 4 5 6 7 8 9 10 SAMPLE AVERAGE 55 47 49 50 52 57 55 48 51 56 SAMPLE RANGE 3 1 5 3 2 6 3 2 2 3

a) What are the x-chart control limits when the machine is working properly?

b) What are the R-chart control limits when the machine is working properly?

c) What seems to be happening? (Hint: Graph the data points.

Run charts may be helpful.)