Chapter 4.2, Problem 13E

A supplier of kerosene has a 150-gallon tank that is filled at the beginning of each week. His weekly demand shows a relative frequency behavior that increases steadily up to 100 gallons and then levels off between 100 and 150 gallons. If Y denotes weekly demand in hundreds of gallons, the relative frequency of demand can be modeled by

$f\left(y\right)=\{\begin{array}{l}y,0\le y\le 1,\\ 1,\text{ 1}<y\le 1.5,\\ 0,\text{ elsewhere}\text{.}\end{array}$

1. a. Find F(y).
2. b. Find P(0 ≤ Y ≤ .5).
3. c. Find P(.5 ≤ Y ≤ 1.2).