A series $2,$ angular contact ball bearing with an inner ring rotating at $800$ RPM is required to have a design life of $26$ kh $.$ The bearing is to be used in light impact machinery and must support a radial load of $675l{b}_f$ with a conservative application factor $($see Table $11-5).$ The reliability goal is $90\%.$

a$.$ Find the multiple of rating life $x_D$ and catalog rating $C_{10}.$

b$.$ Choose the smallest appropriate bearing from Table $11-2.$ Estimate its actual reliability.

c$.$ What would $x_D$ and $C_{10}$ be if the reliability goal had been $99\mathrm{.}9\%?$ Is there a bearing meeting this goal in Table $11-2?$