Question

The board of directors of a company knows that the probability that carbon emissions from the company’s factory exceed the permissible level is 35%. They hire a consultant who uses a carbon footprint calculator to test the emissions level. The test, which has an accuracy rate of 85%, indicates that the factory's carbon emissions are within the permissible level.

Given the test result, the probability that carbon emissions from the factory are actually within the permissible level is .

Answer 1

The answer is 0.9132.

Explanation:

Answer 2

The probability that carbon emissions from the factory are actually within the permissible level is 0.9132

Explanation:

-let x represent when the emissions exceed the permissible level

-let y represent when the emissions does not exceed the permissible level

-let p represent when the test indicate that the factory's carbon emissions exceed the permissible level

-let q represent when the test indicate that the factory's carbon emissions does not exceed the permissible level

Probability that the the factory's carbon emissions exceed the permissible level and the test indicates that the factory's carbon emissions are not within the permissible level P(xq) =0.35*0.15= 0.0525

Probability that the factory's carbon emissions does not exceed the permissible level and the test indicates that the factory's carbon emissions are within the permissible level P(yp) = (1-.35)*0.85=0.65*0.85= 0.5525

the probability that carbon emissions from the factory are actually within the permissible level = 0.5525/(0.5525 + 0.0525) = 0.9132