1.) What is the probability that the industrial plant has an excessive CFR on a given day? 2.) Assume that the government agency in charge of the monitoring of the plant requires the measurement of CFR for 2 days. Moreover, based on existing implementing rules and regulations, any industrial plant will be charged with a violation if an excessive CFR is observed during the 2-day period. What is the probability that the plant will NOT be charged with a violation? 3.) Suppose that the industrial plant decides to limit the probability of violating the 2-day regulation to 1%. What should be the daily mean CFR? Assume that the plant can reduce the mean daily CFR by improving its own in-house chemical process.
The daily flow rate of contaminants from an industrial plant is modeled by a normal random variable with a mean value of 10 units/day and a coefficient of variation of 20%. When the contaminant flow rate (CFR) exceeds 14 units on a given day, it is considered excessive. Assume that CFR between any two days is statistically independent.
1.) What is the probability that the industrial plant has an excessive CFR on a given day?
2.) Assume that the government agency in charge of the monitoring of the plant requires the measurement of CFR for 2 days. Moreover, based on existing implementing rules and regulations, any industrial plant will be charged with a violation if an excessive CFR is observed during the 2-day period. What is the probability that the plant will NOT be charged with a violation?
3.) Suppose that the industrial plant decides to limit the probability of violating the 2-day regulation to 1%. What should be the daily mean CFR? Assume that the plant can reduce the mean daily CFR by improving its own in-house chemical process.
4.) Suppose that there is a new proposal in 2022 to change the regulation such that CFR will be measured for 4 days and that any manufacturing plant will be charged with a violation if the excessive CFR is observed in MORE THAN ONE of the 4 days. Which scheme is better (i.e., less strict) for the manufacturing plant? the 2-day scheme or the 4-day scheme? Justify your answer.
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