The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having the density function The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having the density function
f(x)=20,000/(x+100)3, for x>0, f(x)=0, elsewhere.
Find the probability that a bottle of this medicine will have a shelf life of Find the probability that a bottle of this medicine will have a shelf life of
(a) at least 200 days;(a) at least 200 days;
(b) anywhere from 80 to 120 days.