Benzene, a solvent commonly used to synthesize plastics and found in consumer products such as paint strippers and high-octane unleaded gasoline, has been classified by scientists as a leukemia-causing agent. Let Y be the level (in parts per million) of benzene in the air at a petrochemical plant. Then Y can take on the values 0, 1, 2, 3, ... , 1,000,000 and can be approximated by a Poisson probability distribution. In 1978, the federal government lowered the maximum allowable level of benzene in the air at a workplace from 10 parts per million (ppm) to 1 ppm. Any industry in violation of these government standards is subject to severe penalties, including implementation of expensive measures to lower the benzene level.

a. Suppose the mean level of benzene in the air at petrochemical plants μ = 5 is ppm. Find the probability that a petrochemical plant exceeds the government standard of 1 ppm.

b. Repeat part a, assuming that μ = 2.55. 

c. A study by Gulf Oil revealed that 88% of benzene using industries expose their workers to 1 ppm or less of the solvent. Suppose you randomly sampled 55 of the benzene-using industries in the country and determined Y, the number in violation of government standards. Use the Poisson approximation to the binomial to find the probability that none of the sampled industries violates government standards. Compare this probability to the exact probability computed using the binomial probability distribution.

d. Refer to part c. Use the fact that 88% of benzene-using industries expose their workers to 1 ppm or less of benzene to approximate m, the mean level of benzene in the air at these industries. [Hint: Search Table 4 of Appendix B for the value of m that yields closest to .88.]