The Environmental Protection Agency (EPA) has established national ambient air quality standards in an effort to control air pollution. Currently, the EPA limit on ozone levels in air is 12 parts per hundred million (pphm). A study examined the long-term trend in daily ozone levels in Houston, Texas.* One of the variables of interest is Y, the number of days in a year on which the ozone level exceeds the EPA 12 pphm threshold. The mean number of exceedances in a year is estimated to be 18. Assume that the probability distribution for Y can be modeled with the Poisson distribution.

a. Compute P(Y ≤ 20) .

b. Compute P(5 ≤ Y ≤ 10).

c. Estimate the standard deviation of Y. Within what range would you expect Y to fall in a given year?

d. The study revealed a decreasing trend in the number of exceedances of the EPA threshold level over the past several years. The observed values of Y for the past 6 years were 24, 22, 20, 15, 14, and 16. Explain why this trend casts doubt on the validity of the Poisson distribution as a model for Y. (Hint: Consider characteristic #3 of the Poisson random variable.)