An $*$ chart with three$-$sigma limits has parameters as follows:

UCL $=104$

Center line $=100$

LCL $=96$

n $=5$

Suppose the process quality characteristic being controlled is normally distributed with a true mean of $98$ and a standard deviation of $8.$ What is the probability that the control chart would exhibit lack of control by at least the third point plotted?

$6\mathrm{.}26.$ Consider the $*$ chart defined in Exercise $6\mathrm{.}25.$ Find the ARL, for the chart.