$1-19$ A round cold$-$drawn $1045$ steel rod has a mean strength $\frac{?}{\text{b}\text{a}\text{r}}(S{)}_y=95\mathrm{.}5k$ with a standard deviation of hat$({)}_{S_y}=6\mathrm{.}59k.$ The rod is to be subjected to a mean static axial load of $\frac{?}{\text{b}\text{a}\text{r}}(P)=65$kip with a standard deviation of hat$({)}_p=5\mathrm{.}0$kip. Assuming the strength and load have normal distributions, determine the reliabilities corresponding to the design factors of $($a$)1\mathrm{.}2,($b$)1\mathrm{.}5.$ Also, determine the diameter corresponding to each case.