12.24 Alternative control limits.

American and Japanese practice uses three-sigma control charts. That is, the control limits are three standard deviations on either side of the mean. When the statistic being plotted has a Normal distribution, the probability of a point outside the limits is about 0.003 (or about 0.0015 in each direction) by the 68-95-99.7 rule. European practice uses control limits placed so that the probability of a point out is 0.001 in each direction. For a Normally distributed statistic, how many standard deviations on either side of the mean do these alternative control limits lie?