The Environmental Protection Agency (EPA) issues pollution standards that vitally affect the safety of consumers and the operations of industry (The United States Government Manuul1998-1999). For example, the EPA states that manufacturers of vinyl chloride and similar compounds must limit the amount of these chemicals in plant air emissions to no more than 10 parts per million.

Suppose the mean emission of vinyl chloride for a particular plant is 4 parts per million. Assume that the number of parts per million of vinyl chloride in air samples, x, follows a Poisson probability distribution.

a. What is the standard deviation of x for the plant?

b. Is it likely that a sample of air from the plant would yield a value of x that would exceed the EPA limit?

Explain.

c. Discuss conditions that would make the Poisson assumption plausible.