A Manufacturer of Light Bulbs Wants to Produce Bulbs That $400$

Multiple Choice

A manufacturer of light bulbs wants to produce bulbs that last about $400$ 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 $\int_{0}^{\infty} r(t) d t$ ?

A) $\int_{0}^{\infty} r(t) d t=400$
B) $\int_{0}^{\infty} r(t) d t=2$
C) $\int_{0}^{\infty} r(t) d t=0$
D) $\text { divergent }$
E) $\int_{0}^{\infty} r(t) d t=1$