Given the following process control data for a normally distributed quality variable (three samples of size four each):

Machine		Measurements
#1		15	14	15	12
#2		18	16	20	16
#3		16	17	16	17

What is the sample mean for sample #1? Sample #2? and Sample #3?

If the process is known to have a mean () of 15 and a standard deviation () of 3, what is the mean () of the sampling distribution of sample means for whenever this process is under control? What is the standard deviation ()?

If the process is known to have a mean () of 15 and a standard deviation () 3, what are the three sigma (3) upper and lower control limits for an x-bar chart?

If the process is known to have a mean () of 15 and a standard deviation () of 3, using three sigma control limits found in part c above, do any of the sample means indicate an out-of-control process mean (which ones if any)?