A Lightbulb Company Knows That Its Lightbulbs Have a Lifespan $\left\{ \begin{array} { l l } \frac { A } { ( 2 - x ) ^ { 4 } } & 3 < x < 4 \\0 & \text { else. }\end{array} . \right.$

Short Answer

A lightbulb company knows that its lightbulbs have a lifespan (in thousands of hours) modelled by a random variable with the probability density function $\left\{ \begin{array} { l l } \frac { A } { ( 2 - x ) ^ { 4 } } & 3 < x < 4 \\0 & \text { else. }\end{array} . \right.$ .
(a) Find
(b) If a certain company installs 3 of their lightbulbs at the same time, what is the probability that all three need to be replaced within 3500 hours?