Hi, I would certainly appreciate it if you could please confirm the result I obtained to the following Statistics problem. 1. The problem statement, all variables and given/known data A tank is supplied with fuel once a week. If the fuel (in thousands of liters) that the station sells in a week is a random variable which is distributed with the following density: fx(x) = c(1-x)4 for 0≤x≤1 and 0 otherwise what ought to be the capacity of the tank so that the probability that it is emptied within a week is less than 5%? 2. Relevant equations 3. The attempt at a solution Since x is a random variable, with continuous distribution, it must fulfill the following conditions: f(x)≥0 and ∫f(x)dx between 0 and 1 must be equal to 1. Hence, c = 5. I then found F(x), the cumulative distribution, to be: 0 for x<0, x5 for 0≤x≤1, and 1 for x>1. Which inequality must now be written in order to assure the required condition? Is it x5<0.05, yielding 550 liters?