A machine fills sacks with potatoes which are sold in 3kg bags. An automatic filling machine is set with a mean of 3.2kg and fills with a standard deviation of 30g. An acceptance control scheme is to be set up so that the ARL is at least 155 if the mean remains inside the interval (3200 85)g but less than 3 if the mean drifts outside the interval (3200 112.5)g.

Find the sample size and action limits for the acceptance sampling scheme and verify the ARLs.