What capacity must the tank in Prob. 15 have in order that the probability that the tank will be emptied in a given week be 5%?

Data from Prob. 15

A small filling station is supplied with gasoline every Saturday afternoon. Assume that its volume X of sales in ten thousands of gallons has the probability density f(x) = 6x(1 - x) if 0 ≤ x ≤ 1 and 0 otherwise. Determine the mean, the variance, and the standardized variable.