Suppose a highway weigh-in-motion (WIM) device is used to make sure that vehicle

Question

Suppose a highway weigh-in-motion (WIM) device is used to make sure that vehicles above the maximum allowed gross vehicle weight are signaled to exit at a truck weight station so that they can unload some cargo and come into compliance. When the trucks are truly over the weight limit, the WIM device detects this correctly 96% of the time. However, when trucks are under the weight limit, the WIM device will inaccurately report them as overweight 3% of the time. If 5% of the overall truck traffic tends to be overweight, and if a truck has been signaled to turn off the highway by the WIM device, what is the probability that it is actually overweight?

Explanation / Answer

Probability that correctly indicates truck is overloaded, P(T|O) = 0.96

Probability that incorrectly indicated as overload when it is underloaded, P(T|O') = 0.03

Probability that a random truck will be overloaded, P(O) = 0.05 and P(O') = 0.95

Required probability, P(O|T) = P(T|O)*P(O)/(P(T|O)*P(O) + P(T|O')*P(O'))

P(O|T) = 0.96*0.05/(0.96*0.05 + 0.03*0.95)

P(O|T) = 0.6275

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