Question: Use the reliability model for a catchment basin as provided in Problem to compute the mean C that you would permit for a flow F so that the failure probability does not exceed 0.01. Provide your answer in the form of a mean C/F ratio. Perform parametric analysis by varying the target failure probability as follows: 0.01, 0.005, 0.001, 0.0005, and 0.0001.

Problem: Catchment basins are used to protect residential areas and highways from mud slides. A mudslide basin has a capacity of C, which is a random variable with a COV of 0.2. The expected 25-year maximum inflow is denoted F with a COV of 1.0. Develop an expression for computing the reliability index and the failure probability assuming lognormal probability distributions for both C and F. Compute the reliability index and the failure probability assuming that the mean ratio of C/F is 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8, and 3.0. What mean ratio would you recommend to protect a highway section with average traffic volume of 5000 vehicles per day at an average speed of 50 mph? Discuss and justify your selection.