Suppose a machine for filling kegs with beer is set so that it will generate fillings which form a normal population with mean 15.5 gal and standard deviation 0.20 gal. A control chart will be used in the filling process to control the mean.

a. What lower control limit (LCL) and upper specification limit (UCL) should be used? Assume the sample size is 8, and a level of significance = 0.5%.

b. Calculate the sample size if we want UCL - LCL = 0.2, without changing the significance level.