Refer to the table Factors for Computing Control Chart Limits (3 sigma)LOADING... for this problem. 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 53 grams and a range of 5 grams.

The following table contains the data for a sample size of nequals6 taken during the past 3 hours: Sample 1 2 3 4 5 6 7 8 9 10

x overbar 51 53 52 55 54 54 52 53 51 53

R 4 7 4 5 4 8 3 7 8 3

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

Calculate the upper control limit of the x overbar-chart

Calculate the lower control limit of the x overbar-chart.

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

Calculate the upper control limit of the R-chart.

Calculate the lower control limit of the R-chart.

The process is in control if all sample mean and range values are within the control limits. What seems to be happening? Has the process been in control? Yes or no?