# Thread: Probability of shelf life (in hours)

1. ## Probability of shelf life (in hours)

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

2. Originally Posted by Yan
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
this is asking for $P \{ X \ge 200 \} = \int_{200}^\infty f(x)~dx$

(b) at most 100 hours
this is asking for $P \{ X \le 100 \} = \int_{- \infty}^{100} f(x)~dx = \int_0^{100} f(x)~dx$

(c) anywhere from 80 to120 hours
this is asking for $P \{ 80 \le X \le 120 \} = \int_{80}^{120} f(x)~dx$

i leave it to you to evaluate the integrals. hopefully you can