Final answer:
Seat belts are reported to reduce the risk of crash-related injuries and deaths by about half. Statistical methods can determine the proportion of drivers who regularly wear seat belts, and the force seat belts need to exert in a crash to stop a passenger can also be calculated based on mass and stopping time.
Step-by-step explanation:
When examining the improvement of a person's chance of survival due to wearing a seat belt, various studies and statistical analyses provide insight. For example, the National Highway Traffic Safety Administration (NHTSA) estimates that seat belts reduce the risk of crash-related injuries and deaths by about half. Additionally, using seat belts is one of the most effective ways to save lives and reduce injuries in crashes.
To accurately assess the population proportion of drivers who wear seat belts, statistical methods are employed. If we were to conduct a survey to determine this proportion with 95 percent confidence and wanted to estimate the population proportion to within 0.03, we'd need a certain minimum number of responses. Furthermore, to achieve a confidence level greater than 95 percent in a new survey, we would have to increase the sample size, since higher confidence levels require larger sample sizes to ensure the same margin of error.
Utilizing data and statistics, we might find in a random survey of 400 drivers, if 320 claim they always buckle up, we can estimate the proportion of all drivers who do. Using this data, we can calculate a 95 percent confidence interval to understand the range in which the true population proportion lies.
The use of seat belts can significantly reduce the impact forces experienced during car accidents. For instance, a seat belt can help distribute forces of a crash across the stronger parts of the person's body, like the hips and shoulders. If a car crashes into a tree and stops in 0.26 seconds and the passenger is 70 kg, we can calculate the force the seat belt needs to exert to halt the passenger safely.