i$)$ A pneumatic displacement gage has $d_1=0\mathrm{.}762mm$ and $d_2=1\mathrm{.}575mm.$ The supply

pressure is $68919\mathrm{.}7$ Pa with a random fluctuation of $+-483Pa,$ and the differential

pressure $P_d-P_a$ is measured with a water manometer that may be read with an

uncertainty of $12\mathrm{.}44$ Pa $.$ Calculate the uncertainty in the dimensional measurement

using both: a$)$ non$-$analytical method, and b$)$ analytical method.