Speeding New Jersey drivers. A certain stretch of highway on the New Jersey Turnpike has a posted speed limit of 60 mph. A survey of drivers on this portion of the turnpike revealed the following facts (reported in The Washington Post, Aug. 16,1998):
(1) 14% of the drivers on this stretch of highway were African-Americans
(2) 98% of the drivers were exceeding the speed limit by at least 5 mph (and thus were subject to being stopped by the state police)
(3) Of these violators, 15% of the drivers were African-Americans
(4) Of the drivers stopped for speeding by the New Jersey state police, 35% were African-Americans
a. Convert each of the reported percentages into a probability statement.
b. Find the probability that a driver on this stretch of highway is African-American and exceeding the speed limit.
c. Given that a driver on this stretch of highway is exceeding the speed limit, what is the probability that the driver is not African-American?
d. Given that a driver on this stretch of highway is stopped by the New Jersey state police, what is the probability that the driver is not African-American?
e. For this stretch of highway, are the events (African-American driver and {Driver exceeding the speed limit} independent (to a close approximation)? Explain.
f. Use the probabilities in The Washington Post report to make a statement about whether African-Americans are stopped more often for speeding than would be expected on this stretch of turnpike.
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