Prob 1. Prob 2. Prob 3. Solve problem 1 again using the lognormal assumption of the load. Prob 4. Prob 5. If the load S applied on a bar is assumed to be a normal distribution with a mean of 200 MPa and a standard deviation of 20 MPa. The bar's ultimate strength R is also a normal distribution with a mean of 210 MPa with a standard deviation of 5 MPa. It is known that a summation or subtraction of two normal distribution also follows the normal distribution. Please calculate the failure probability of the bar. Hint: The failure happens when difference of the bar strength and the applied load is less than zero