A small petrol station is supplied with petrol once a week. Assume that its volume X of potential sales (in units of 10, 000 litres) has the probability density function f(x) = 6(r – 2)(3 – x) for 2 < a< 3 and f(x) = 0 otherwise. Determine the mean and the variance of this distribution. What capacity must the tank have for the probability that the tank will be emptied in a given week to be 5%?

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