The Environmental Protection Agency (EPA) limits the amount of vinyl chloride 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 x of parts per million of vinyl chloride in air samples 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.