Q$3$ A certain application requires a ball bearing with the inner ring rotating, with a design life of $30000$ hour at the speed of $300re\frac{v}{m}in.$ The radial load is $1\mathrm{.}898$ kN and an application factor of $1\mathrm{.}2$ appropriate. The reliability goal is $0\mathrm{.}90.$ the catalogue rating $C_{10}.$ Choose a $02-$series deep$-$groove ball bearing from Table $($Refer table $11-2$ from Shigley$),$ and estimate the reliability in use.