Question

(11 points) On any given day, the probability that a large local river is polluted by carbon tetrachloride is 0.1. Each day, a test is conducted to determine whether the river is polluted by carbon tetrachloride. This test has proved correct 82 percent of the time. Use this information and a theoretical group of 10,000 days to construct a table for this testing scenario. Round all answers to four decimal places. Polution presentTest Positive Test Negative Total Yes No Total 10,000 1. What proportion of days does the test indicate carbon tetrachloride pollution? 2. Suppose that on a particular day the test indicated carbon tetrachloride pollution. What is the probability that such pollution actually exists? 3. What percentage of days where the test is negative will the river actually be polluted?

Answer 1

from given data:

	test positive	test negative	total
Yes	820	180	1000
No	1620	7380	9000
total	2440	7560	10000

1)P(test positive)=2440/10000=0.2440

2)P(pollution given test positive)=(820/2440)=0.3361

3)P(pollution given test negative)=(180/7560)*100=2.3810%