Question:

A service station will be supplied with gasoline once a week. Its weekly volume of sales, x, in 10,000 of gallons, is described by the probability density function

\[\text{f(t)}=\text{ t}{{e}^{\text{-}\frac{{{\text{t}}^{\text{2}}}}{\text{2}}}}\text{ for t}>0\]

Determine the capacity if its underground tank so that the probability that its supply will be exhausted in a given week is to be 0.01.

What is the expected sales volume?