The shelf life, in days, for bottles of a certain medicine is a random variable that has the density function

$\displaystyle

f(x) = \frac{20000}{(x+100)^3}, x > 0 $

0, elsewhere

What is the probability that a bottle of this medicine will a shell life of

atleast 200 days?

My professor said that this is a continuous random variable and gave this integral: $\displaystyle \int^{\infty}_{200} \frac{20000}{(x+100)^3} dx =

\frac{-10000}{(x+100)^2} $ from 200 to infinity

I say the random variable is discrete because the number of days is countable.