$2.$ A round cold$-$drawn $1060$ steel rod is machined with high precision machining and has a

mean yield strength Sy $=98\mathrm{.}5$ kpsi with a standard deviation of $3\mathrm{.}3$ kpsi. The rod is to be

subjected to a mean static axial load of P $=70$ kip with a standard deviation of $10$ kip.

Assuming the strength and load have normal distributions, what value of the design

factor nd corresponds to a reliability of $0\mathrm{.}95$ against yielding? Determine the

corresponding diameter of the rod for $0\mathrm{.}95$ reliability. As a mechanical designer, in what

ways you can improve this design explain your answer. $(5$ points$)$