The shelf life (in hours) of a certain perishable pack-aged food is a random variable whose probability density function is given byf(x) =⎧⎪⎪⎨⎪⎪⎩20,000(x + 100)3 for x > 00 elsewhere Find the probabilities that one of these packages will havea shelf life of(a) at least 200 hours;(b) at most 100 hours;(c) anywhere from 80 to 120 hours.

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The shelf life (in hours) of a certain perishable pack-
aged food is a random variable whose probability density
function is given by
f(x) =

⎪⎪⎨
⎪⎪⎩
20,000
(x + 100)3 for x > 0
0 elsewhere
Find the probabilities that one of these packages will have
a shelf life of(a) at least 200 hours;
(b) at most 100 hours;
(c) anywhere from 80 to 120 hours.
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