3. One of the variables measured by the National Highway Traffic Safety Administ

Question

3. One of the variables measured by the National Highway Traffic Safety Administration in their crash test for new cars 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 rating, the more sever the injury. The head injury ratings can be shown to be approximately normally distributed with a mean of 605 points and a standard deviation of 185 points. One of the crash-tested cars is selected at random from the data and the driver's head injury rating is observed. a) Find the probability that the rating will fall between 500 and 700 points. (10 pts.) b) Find the probability that the rating will be less than 850 points. (10 pts.) c) What rating will only 10% of the crash-tested cars exceed? (10 pts.)

Explanation / Answer

The normal distribution params are given by :

Mean = 605

Stdev = 185

a. P(500<X<700) = P((500-605)/185<Z<(700-605)/185) = .696-.285 = .411

b. P(X<850) = P(Z< (850-605)/185) = P(Z<1.324) = .9066

c. P(X<c) = .10

So, (c-605)/185 = -1.28

c = -1.28*185 +605 = 368.2

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.