Refer to the previous exercise. When a machine for dispensing a cola drink into bottles is in statistical control, the amount dispensed has a mean of 500 ml (milliliters) and a standard deviation of 4 ml.
a. In constructing a control chart to monitor this process with periodic samples of size 4, how would you select the target line and the upper and lower control limits?
b. If the process actually deteriorates and operates with a mean of 491 ml and a standard deviation of 6 ml, what is the probability that the next value plotted on the control chart indicates a problem with the process, falling more than 3 standard deviations from the target? What do you assume in making this calculation?