Q$1$: A certain business process is under its management scrutiny for cost reduction purposes. A critical measurement to be targeted is $x,$ which is historically distributed as normal with a mean of $15\mathrm{.}0$ units and a standard deviation of $3\mathrm{.}0$ units. A process improvement initiative is necessary when the sample mean of $16$ random observations exceeds above the population mean by more than $\frac{1}{2}$ of the population standard deviation. With no other changes to this process, what percentage of times must they initiate a call for process improvement?