The shelf life (in hours) of a certain perishable packaged food is a random variable whose probability density function is given by

f(x)=20,000/((x+100)^3) for x>0 and =0 elsewhere

Find the probabilities that one of these packages will have a shelf lift of

(a) at least 200 hours

(b) at most 100 hours

(c) anywhere from 80 to120 hours