Chapter 11.2, Problem 64E

Shelf life. Repeat Problem 63 if

$f\left(x\right)=\{\begin{array}{cc}200x/{\left(100-x^2\right)}^2& \text{if }x\ge 0\\ 0& \text{otherwise}\end{array}$

63.    Shelf life. The shelf life (in days) of a perishable drug is a continuous random variable with probability density function given by

$f\left(x\right)=\{\begin{array}{cc}800x/{\left(400+x^2\right)}^2& \text{if }x\ge 0\\ 0& \text{otherwise}\end{array}$

(A)    What is the probability that the drug has a shelf life of at most 20 days?

(B)    What is the probability that the shelf life exceeds 15 days?

(C)    If the user wants the probability that the drug is still good to be .8, when is the last time it should be used?