A round cold-drawn 1045 steel rod has a mean strength S̅_y = 95.5 kpsi with a standard deviation of σ̂ = 6.59 kpsi. The rod is to be subjected to a mean static axial load of P̅ = 65 kip with a standard deviation of σ̂_P  = 5.0 kip. Assuming the strength and load have normal distributions, determine the reliabilities corresponding to the design factors of 

(a) 1.2

(b) 1.5. 

Also, determine the diameter corresponding to each case.