What is the reasoning behind setting the upper and lower control limits $+-3$ from the mean?

a$.95\mathrm{.}45\%$ of the time, the sample averages will fall within $+-3x$ if the process has only natural variation

b$.$ The limits of the Z table are set at $+-3.$

c$.$ We know that $99\mathrm{.}73\%$ of assignable variation is contained within $+-3,$ and thus any data point outside

of the limits is likely due to natural variation.

d$.$ We know that $99\mathrm{.}73\%$ of natural variation is contained within $+-3,$ and thus any data point outside of

the limits is likely due to assignable variation.