Chapter 6.2, Problem 24E

In Problem 22, find d so that the probability of a randomly selected laser pointer battery lasting d years or less is .5.

22. The shelf life (in years) of a laser pointer battery is a continuous random variable with probability density function

     $f(x)=\{\begin{array}{cc}1/{(x+1)}^2& ifx\ge 0\\ 0& \text{otherwise}\end{array}$

1. (A)  Find the probability that a randomly selected laser pointer battery has a shelf life of 3 years or less.
2. (B)  Find the probability that a randomly selected laser pointer battery has a shelf life of from 3 to 9 years.
3. (C)  Graph y = f(x) for [0, 10] and show the shaded region for part (A).