Chapter 12, Problem 9RE

Probability of Gasoline Sales A certain gas station sells $X$ thousand gallons of gas each week. Suppose that the cumulative distribution function for $X$ is $F\left(x\right)=1-\frac{1}{4}\left(2-x^2\right),0\le x\le 2$

If the tank contains 1.6 thousand gallons at the beginning of the week, find the probability that the gas station will have enough gas for its customers throughout the week.

How much gas must be in the tank at the beginning of the week to have a probability of $.99$ that there will be enough gasoline for the week?

Compute the density function for $X$.