A weather balloon has an absolute$-$pressure sensor attached. On the ground the sensor reads PA $=1\mathrm{.}2010^5$ Pa$.$ At a height of h $=993$ m$,$ the sensor reads PB $=9\mathrm{.}2510^4$ Pa$.$

Part$($a$)$ Assuming air is an incompressible fluid, enter an expression for an estimate of the density of air, in terms of the defined quantities and the acceleration due to gravity, g$.$

Part $($b$)$ Calculate the density of air, in kilograms per cubic meter, assuming it is an incompressible fluid.