A two$-$bar symmetric pin$-$connected truss shown on right is subject to a vertical load P$.$

$($a$)$ If the load P has a normal distribution with $=10,000$

lbs and $=1,000$ lbs$.$ Select the cross$-$sectional area A of the steel bars $($yield strength $=30,000$ psi$)$ so that the probability of failure of the truss does not exceed $0\mathrm{.}006.$ Then use the obtained A to determine the factor of safety if P $=10,000$ lbs$.$ All parameters except the load are deterministic.

$($b$)$ If the yield strength is also random with $=30,000$ psi and $=3,000$ psi, determine A so that the probability of failure of the truss does not exceed $0\mathrm{.}006.$ With the obtained A$,$ determine the factor of safety if $=10,000$ lbs and $=30,000$ psi.