Science:Math Exam Resources/Courses/MATH103/April 2017/Question 09 (b)/Solution 1

The median age of mortality is the age $x$ at which the probability $C(x)$ that a jellyfish dies before reaching age $x$ equals to the probability $1-C(x)$ that a jellyfish dies after reaching age $x$. In other words, we need to find the solution to

$C(x)=1-C(x)\iff C(x)={\frac {1}{2}}$.

From part (a), we get $C(x)={\frac {2}{\pi }}\arctan(x)$, therefore, we now solve

${\frac {4}{\pi }}\arctan(x)=1\iff x=\tan({\frac {\pi }{4}})=1$.

Hence, the median age of mortality is $\color {blue}1$