A question

A petrol pump is supplied with petrol once a day. If its daily volume of sales (X) in thousands of litre is distributed by : f(x)=5(1-x)^4, 0 <= x <= 1 what must be the capacity of its tank in order that the probability that its supply will be exhausted in a given day shall be 0.01?

Thank you in advance.

We have to find the distribution.

You did not state specifically, but it would appear the probability density is \(\displaystyle 5(1-x)^{5}\).

We want the probability \(\displaystyle P(X>V)=.01\). Where X is their sales and V is the tank volume.

\(\displaystyle F(t)=5\int_{0}^{t}(1-x)^{5}dx\)

\(\displaystyle P(X>V)=1-F(V)\)

Can you finish?.

Thank you very much galactus. Yes I can take it from here.