Question

Suppose the concentration of a certain pollutant is uniformly distributed in the range of 4 to 20 ppm (parts per million). if a concentration in excess of 15 ppm is considered toxic, what is the probability that a specimen will yield a toxic concentration level

Answer 1

Uniform probability?  Here the probability function graph is a rectangle of length 20-4 (or 16) and width / height of 1/16.  Note that the area under the graph from x=4 to x=20 is 1 (which is always the case when we're discussing probability functions).  The area under the graph from 15 to 20 is (20-15)(1/16), or
5(1/16), or 5/16.  Thus, the probability that a specimen will yield a toxic concentration level is 5/16.

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