One of the variables the National Highway Traffic Safety Administration (NHTSA)

Question

One of the variables the National Highway Traffic Safety Administration (NHTSA) measures is the severity of a driver's head injury when the car is in a head-on collision with a fixed barrier while traveling at 35 miles per hour. The more points assigned to the head injury, the more severe the injury. The probability that the head injury rating is more than 700 points is approximately 33%. It can be shown that the head injury ratings are normally distributed with a standard deviation of 185 points. What is the probability that a crash test will result in a head injury rating of less than 600?

Explanation / Answer

inverse z(1-.333) ˜ 0.430727 z = (x-)/ 0.430727 = (700 -)/185 79.6846 = 700 - = 620.315 z = (600-620.315)/185 z ˜ -0.109813 P(Rating < 600) = P(z

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