1. The problem statement, all variables and given/known data In considering the safety of building, the total force acting on the columns of the building must be examined. This would include the effects of the dead load, D, due to weight of the structure, the live load, L, due to human occupancy, movable furniture and the like, and the wind load, W. Assume that the load effects on the individual columns are statistically independent Normal random variables with: mean of D (dead load) = 4.2 kips, standard deviation = 0.3 kips mean of L (live load ) = 6.5 kips, standard deviation = 0.8 kips mean of W (wind load) = 3.4 kips, standard deviation = 0.7 kips (a) Determine the mean and standard deviation of the total load acting on a column. (b) Suppose the strength of the column is also Normal with mean equal to 1.5 times of the total mean load and the coefficient of variation of the strength is 15%. A column fails if the strength is less than the total load. What is the probability of failure of the column? 2. Relevant equations 3. The attempt at a solution Part a. Yielded 14.1 kips as the mean, and 1.1045 for the deviation, and is the correct answer. As for part b, from what i see, the picture for me seems to be 2 normal distributions with their tails overlapping. Any suggestions on how to approach it would be appreciated (hopefully without the use of the normal distribution's equation, i've done it using that and its a double integral of the cumulative distribution density function.. and long enough to be rather annoying).