Question

A breathalyzer test is used by police in an area to determine whether a driver's blood...

A breathalyzer test is used by police in an area to determine whether a driver's blood alcohol content (BAC) is above the legal limit. The device is not totally reliable: 3.9% of drivers who have not consumed too much alcohol give a BAC reading from the breathalyzer as being above the legal limit, while 11.8% of drivers who have consumed too much alcohol will give a BAC reading below that level. Suppose that in fact, 5.8% of drivers have consumed too much alcohol to drive legally, and the police stop a driver at random.

Use this information and a theoretical group of 10,000 drivers to construct a table for this testing scenario. Round all answers to four decimal places.

Consumed too much alcohol to drive legally BAC reading is above legal limit BAC reading is below legal limit Total
Yes
No
Total 10,000

1. What proportion of drivers will have a BAC reading showing them to be above the legal limit?

2. Suppose that a randomly stopped driver has a reading above the legal limit. What is the probability that they have consumed too much alcohol to drive safely?

3. What percentage of drivers who test below the legal limit will actually have consumed too much alcohol to drive safely? %

Math   Statistics-And-Probability   
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