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a. Compute P(Y < 20).

a. Compute P(Y < 20).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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Please answer a-d. Thanks

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 <s 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 distribu- tion as a model for Y. (Hint: Consider characteristic #3 of the Poisson random variable.)
Transcribed Image 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 <s 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 distribu- tion as a model for Y. (Hint: Consider characteristic #3 of the Poisson random variable.)
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