Final answer:
The carrier designates the 7 or 14 day cycle a truck driver must follow according to federal hours of service regulation. The probability of driving more than or between specific mile ranges can be calculated using the uniform distribution. The 90th percentile gives the mileage for the highest 10 percent of days.
Step-by-step explanation:
The federal hours of service regulation is governed by the government regulation. Therefore, the cycle that a driver must follow, whether it is a 7 or 14 day cycle, is designated by the carrier's choice, not the driver's preference, union agreement, or the government directly.
Now, addressing the questions based on the information provided:
- The probability that the truck driver goes more than 650 miles in a day, given a uniform distribution between 300 and 700 miles, can be calculated and is found to be a fraction of the total possible range since 650 miles is near the upper limit of the range.
- The probability that the truck driver goes between 400 and 650 miles in a day falls within a larger portion of the total range, and thus the probability is higher than the former scenario.
- On the 10 percent of days with the highest mileage, the truck driver will travel at least a certain number of miles which can be determined by finding the 90th percentile of the uniform distribution.
Understanding the distribution and calculation of probabilities for continuous random variables like the miles driven by a truck driver is essential in industries relying on logistics and transportation.