Final answer:
The statement about the 7 day cycle and 36 hours off-duty time is false; FMCSA regulations often require a 34-hour restart. The probabilities of a truck driver's miles can be calculated using a uniform distribution, and the highest 10 percent of mileage days can be identified with percentiles.
Step-by-step explanation:
The statement "As soon as a driver who is following a 7 day cycle accumulates 70 hours of on-duty time in the cycle he/she must take 36 hours off-duty before driving a commercial motor vehicle" is false. Under current Federal Motor Carrier Safety Administration (FMCSA) regulations, truck drivers operating under the 70-hour/7-day cycle may be required to take a rest period, but the specific duration of the off-duty time can vary and is not necessarily 36 hours. Instead, they may be required to follow the 34-hour restart rule, which allows them to reset their 70-hour clock.
Regarding the other questions:
- 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 by finding the area of the distribution curve above 650 miles.
- The probability of the truck driver going between 400 and 650 miles is found by calculating the area under the curve between these two values.
- The mileage that the truck driver travels on the 10 percent of days with the highest mileage can be determined using percentiles of the distribution.