3. Ambient air quality. The Environmental Protection Agency (EPA) has established national ambient air quality stan- dards in an effort to control air pollution. Currently, the EPA limit on ozone...


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3. Ambient air quality. The Environmental Protection Agency<br>(EPA) has established national ambient air quality stan-<br>dards in an effort to control air pollution. Currently, the<br>EPA limit on ozone levels in air is 12 parts per hundred<br>million (pphm). A study examined the long-term trend in<br>daily ozone levels in Houston, Texas.* One of the vari-<br>ables of interest is Y, the number of days in a year on<br>which the ozone level exceeds the EPA 12 pphm threshold.<br>The mean number of exceedances in a year is estimated to<br>be 18. Assume that the probability distribution for Y can<br>be modeled with the Poisson distribution.<br>a. Compute P(Y <s 20).<br>b. Compute P(5 < Y < 10).<br>c. Estimate the standard deviation of Y. Within what<br>range would you expect Y to fall in a given year?<br>d. The study revealed a decreasing trend in the number of<br>exceedances of the EPA threshold level over the past<br>several years. The observed values of Y for the past 6<br>years were 24, 22, 20, 15, 14, and 16. Explain why this<br>trend casts doubt on the validity of the Poisson distribu-<br>tion as a model for Y. (Hint: Consider characteristic #3<br>of the Poisson random variable.)<br>

Extracted text: 3. Ambient air quality. The Environmental Protection Agency (EPA) has established national ambient air quality stan- dards 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 vari- ables 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

Jun 11, 2022
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