A Manufacturer of Light Bulbs Wants to Produce Bulbs That $F ( t )$

Short Answer

A manufacturer of light bulbs wants to produce bulbs that last about 700 hours but, of course, some bulbs burn out faster than others. Let $F ( t )$ be the fraction of the company's bulbs that burn out before $t$ hours. $F ( t )$ lies between 0 and 1 .
Let $r ( t ) = F ^ { \prime } ( t )$ . What is the value of $\int _ { 0 } ^ { \infty } r ( t ) d t$ ?