solve Many companies must monitor the effluent that is discharged from their pla

Question

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Many companies must monitor the effluent that is discharged from their plants into rivers and waterways. In some states, it is the law that some substances have water-quality limits that are below the limit of detection, L, for the current method of measurement. The effluent is judged to satisfy the quality limit if every test specimen is below the limit of detection L. Otherwise it will be declared to fail compliance with the quality limit. Suppose the water does not contain the contaminant of interest but that the variability in the chemical analysis still gives a 1% chance that a measurement on a test specimen will exceed L. Find the probability that neither of two specimens, both free of the contaminant, will fail to be in compliance.

Explanation / Answer

Let

L = below the limit of detection
F = fails compliance
P = passes compliance

Hence, as for a specific specimen

P(F|L) = 0.01

Then

P(P|L) = 1 - 0.01 = 0.99

Hence, if both passes, the test

P(both pass) = 0.99*0.99 = 0.9801 [ANSWER]

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