a) To estimate the mean stopping distance within 2 feet of the true mean with 95% confidence, we need to calculate the maximum allowable error. With a $12,000 budget and $100 per observation, we can determine if there are sufficient funds to meet this requirement.
b) Meeting the regulatory agency's 95% confidence level for the mean stopping distance within 2 feet while staying within the $12,000 budget may require adjusting sample size or finding cost-effective study methods. Failure to comply could lead to certification delays or legal consequences for the manufacturer.
In summary:
- For part a, we assess if there are enough funds to estimate the mean stopping distance accurately.
- In part b, we discuss the challenges of meeting regulatory requirements within budget constraints, highlighting potential repercussions for the manufacturer.
