Refer to the National Highway Traffic Safety Administration (NHTSA) crash test data for new cars, presented in Exercise 2.190 (p. 107). One of the variables measured 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 severe is 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 randomly selected 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.
b. Find the probability that the rating will fall between 400 and 500 points.
c. Find the probability that the rating will be less than 850 points.
d. Find the probability that the rating will exceed 1,000 points.
e. What rating will only 10% of the crash-tested cars exceed?