I am trying to solve the following testing problem, which can be rephrased as:
A load of cargo contains 49 boxes where the weight of a box follows a distribution with mean µ = 205 pounds and standard deviation σ = 15 pounds.
What is the probability that all 49 boxes can be safely loaded onto the elevator which can transport a maximum of 9800 pounds.
Here are my thoughts: I need to find a the value of a cumulative distribution function $CDF(9800, µ_1, σ_1)$, where $µ_1 = 49 * µ$, $σ_1 = 49 * σ$. So I get the probability of 0.36, which is not correct.
Be careful, standard deviation of the sum is not the sum of the standard deviation, it is the square root of the sum of variances.