# Normal distributions: Probabilities and percentiles

The highway police in a certain state are using aerial surveillance to control speeding on a highway with a posted speed limit of 55 miles per hour. Police officers watch cars from helicopters above a straight segment of this highway that has large marks painted on the pavement at 1-mile intervals. After the police officers observe how long a car takes to cover the mile, a computer estimates that cars speed. Assume that the errors of these estimates are normally distributed with a mean of 0 and a standard deviation of 3.41 miles per hour.

a. The state police chief has directed his officers not to issue a speeding citation unless the aerial units estimate of speed is at least 66 miles per hour. What is the probability that a car travelling at 58 miles per hour or slower will be cited for speeding?

b. Suppose the chief does not want his officers to cite a car for speeding unless they are 99% sure that it is travelling at 58 miles per hour or faster. What is the minimum estimate of speed at which a car should be cited for speeding?

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#### Solution Summary

This solution shows how to calculate probabilities and find percentiles of a normal distribution