Question 1180900: The National Occupant Protection Use Survey (NOPUS) was conducted to provide probability-based data on motorcycle helmet use in the United States. The survey was conducted by sending observers to randomly selected roadway sites where they collected data on motorcycle helmet use, including the number of motorcyclists wearing a Department of Transportation (DOT)-compliant helmet (National Highway Traffic Safety Administration website, January 7, 2010). Sample data consistent with the most recent NOPUS are shown below.
The National Occupant Protection Use Survey (NOPUS
a. Use the data to compute the probability that a motorcyclist wears a DOT-compliant helmet. Round your answer to four decimal places.
b. The probability that a motorcyclist wore a DOT-compliant helmet five years ago was 0.48, and last year this probability was 0.63. Would the National Highway Traffic Safety Administration be pleased with the most recent survey results shown above?
c. What is the probability of DOT-compliant helmet use by region of the country? Round your answer to four decimal places.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to analyze the motorcycle helmet use data:
**a. Probability of DOT-compliant helmet use:**
1. **Total observations:** Add up all the observations from each region: 1162 + 944 + 1092 + 1048 = 4246
2. **Total DOT-compliant helmets:** Add up the number of DOT-compliant helmets in each region: 928 + 798 + 873 + 848 = 3447
3. **Probability:** Divide the number of DOT-compliant helmets by the total number of observations: 3447 / 4246 ≈ 0.8118
**Therefore, the probability that a motorcyclist wears a DOT-compliant helmet is approximately 0.8118.**
**b. NHTSA's reaction:**
* The current probability of DOT-compliant helmet use is 0.8118.
* Five years ago, it was 0.48.
* Last year, it was 0.63.
The NHTSA would likely be *very* pleased with the most recent results. The probability has increased significantly from both five years ago and last year. This suggests that their efforts to promote helmet use are potentially having a positive impact.
**c. Probability of DOT-compliant helmet use by region:**
To calculate the probability for each region, divide the number of DOT-compliant helmets in that region by the total number of observations in that region:
* **Northeast:** 928 / 1162 ≈ 0.7986
* **Midwest:** 798 / 944 ≈ 0.8453
* **South:** 873 / 1092 ≈ 0.8000
* **West:** 848 / 1048 ≈ 0.8092
**Here's a summary table:**
| Region | DOT-Compliant Helmets | Total Observations | Probability |
| --------- | -------------------- | ------------------ | ----------- |
| Northeast | 928 | 1162 | 0.7986 |
| Midwest | 798 | 944 | 0.8453 |
| South | 873 | 1092 | 0.8000 |
| West | 848 | 1048 | 0.8092 |
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