A new analytical method to detect pollutants in water is being
tested. This new method of chemical analysis is important because,
if adopted, it could be used to detect three different contaminates
- organic pollutants, volatile solvents, and chlorinated compounds
- instead of having to use a single test for each pollutant. The
makers of the test claim that it can detect high levels of organic
pollutants with 99.3% accuracy, volatile solvents with 99.97%
accuracy, and chlorinated compounds with 89.8% accuracy. If a
pollutant is not present, the test does not signal. Samples are
prepared for the calibration of the test and 60% of them are
contaminated with organic pollutants, 27% with volatile solvents,
and 13% with traces of chlorinated compounds. A test sample is
selected randomly.
(a) What is the probability that the test will signal?
(b) If the test signals, what is the probability that the
chlorinated compounds are present?
Carry out all calculations exactly, then round the final answers to
four decimal places (e.g. 98.7654).
a)
probability that the test will signal =0.6*0.993+0.27*0.9997+0.13*0.898 =0.9825\
b)
probability that the chlorinated compounds are present given test signals =0.13*0.898/0.9825 =0.1188
A new analytical method to detect pollutants in water is being tested. This new method of...
A new analytical method to detect pollutants in water is being tested. This new method of chemical analysis is important because, if adopted, it could be used to detect three different contaminates organic pollutants, volatile solvents, and chlorinated compounds instead of having to use a single test for each pollutant. The makers of the test claim that it can detect high levels of organic pollutants with 99.4% accuracy, volatile solvents with 99.90% accuracy and ch onnated compounds with 89.89 accuracy...
A new analytical method to detect pollutants in water is being tested. This new method of chemical analysis is important because, if adopted, it could be used to detect three different contaminants—organic pollutants, volatile solvents, and chlorinated compounds—instead of having to use a single test for each pollutant. The makers of the test claim that it can detect high levels of organic pollutants with 99.7% accuracy, volatile solvents with 99.95% accuracy, and chlorinated compounds with 89.7% accuracy. If a pollutant...