Answer to Question #47265 in Statistics and Probability for Marshal

Question

A new analytical method to detect pollutants in water is being tested. 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 99.6% accuracy, volatile solvents with 99.94% 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?