Question

Type the correct answer in the box. Round your answer to the thousandth place.

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 accuracy of the test is 85%.

The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is __________

Answer 1

The probability that the emissions are within the permissible level and the test incorrectly predicts the opposite is 0.098 or 9.75% after rounding to the thousandth place.

Step-by-step explanation:

The probability that carbon emissions from the factory are within the permissible level is the complement of the probability that they exceed the permissible level, which is 100% - 35% = 65% or 0.65. Given that the test has an accuracy of 85%, the probability that the test incorrectly predicts the emissions to be over the permissible level when they are not (a false positive) is 15% or 0.15. Therefore, the probability that emissions are within the permissible level and the test incorrectly predicts the opposite is the product of the two probabilities: 0.65 * 0.15 = 0.0975 or 9.75% when expressed as a percentage. To provide the answer to the thousandth place as required, we express this as 0.098.

Answer 2

The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is 19.338% (Rounding to the next thousandth place)

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Probability that carbon emissions from the company’s factory exceed the permissible level = 35% = 0.35

Accuracy of the test of emissions level = 85% = 0.85

2. The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is?

These two events, carbon emissions from the company’s factory and the accuracy of the test are independent events, therefore:

Probability that carbon emissions from the factory are within the permissible level = 1 - 0.35 = 0.65

Probability that the test predicts the opposite to be true = 0..35 * 0.85 = 0.2975 (The opposite is that the carbon emissions from the company exceed the permissible level)

Probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is:

0.65 * 0.2975 = 0.193375

The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is 19.338% (Rounding to the next thousandth place)