Crash tests on new cars.The National Highway Traffic Safety Administration (NHTSA) crash-tests new car models to determine how well they protect the driver and front-seat passenger in a head-on collision. The NHTSA has developed a “star” scoring system for the frontal crash test, with results ranging from one star (*) to five stars (*****). The more stars in the rating, the better the level of crash protection in a head-on collision. The NHTSA crashtest results for 98 cars (in a recent model year) are stored in the accompanying data file.
a. The driver-side star ratings for the 98 cars are summarized in the Minitab printout shown below. Use the information in the printout to form a pie chart. Interpret the graph.
Tally for Discrete Variables: DRIVSTAR |
DRIVSTAR | Count | Percent |
2 3 4 5 N = | 4 17 59 18 98 | 4.08 17.35 60.20 18.37 |
b. One quantitative variable recorded by the NHTSA is the driver’s severity of head injury (measured on a scale from 0 to 1,500). The mean and standard deviation for the 98 driver head-injury ratings are displayed in the Minitab printout below. Give a practical interpretation of the mean.
Descriptive Statistics: DRIVHEAD
|
Variable | N | Mean | StDev | Minimum | Q1 | Median | Q3 | Maximum |
DRIVHEAD | 98 | 603.7 | 185.4 | 216.0 | 475.0 | 605.0 | 724.3 | 1240.0 |
C. Use the mean and standard deviation to make a statement about where most of the head-injury ratings fall.
d..Find the z-score for a driver head-injury rating of 408. Interpret the result.