In a machine you have designed, you need a ball bearing that can rotate at a speed of $350$ rpm$,$ has a design life of $25$ kh$,$ and has a rotating inner ring. The radial load is $2\mathrm{.}5$ kN$.$ The application factor $1\mathrm{.}2$ is suitable for operating conditions. The reliability target is $0\mathrm{.}90.$ Determine the required catalogue life $($Xo$)$ and catalogue life C to be entered in the bearing table. Select the $02$ series deep groove ball bearing from the required catalogue $($table$)$ in your book and estimate its reliability in use.