Final answer:
None of the options provided (a through d) directly reflect the correct Hours of Service regulation, which permits a truck driver to drive a maximum of 11 hours after 10 consecutive hours off duty, but a 30-minute break is required after 8 cumulative hours of driving. No Option is correct.
Step-by-step explanation:
According to the Hours of Service regulations currently in effect, one truck driver can drive for a maximum of 11 hours after 10 consecutive hours off duty. However, they must take a 30-minute break if they have driven for a period that totals 8 cumulative hours without at least a 30-minute interruption. Thus, the correct answer to the question is none of the options listed directly (a through d). The 11-hour limit is the allowed driving time within a 14-hour workday, after which the driver must be off duty for 10 consecutive hours.
When it comes to the probability that a truck driver goes more than 650 miles in a day where the number of miles is uniformly distributed between 300 and 700, this can be calculated as:
Subtract the value 650 from 300 to find the range of values (which is 350 miles).
The length of the interval from 650 to 700 is 50 miles.
Divide the length of the interval of interest (50 miles from 650 to 700) by the total range (350 miles).
Therefore, the probability is 50/350 or approximately 0.143, or 14.3%.
For the question regarding the probability that the truck driver goes between 400 and 650 miles, we follow a similar approach:
Subtract 400 from 650, which gives us a 250-mile interval.
Divide 250 by the total range of 350 miles.
The probability for this scenario is 250/350 or approximately 0.714, or 71.4%.
To find out at least how many miles the truck driver travels on the 10 percent of days with the highest mileage, we calculate the 90th percentile for the mileage:
Since it's a uniform distribution, the 90th percentile is found by taking 90% of the range added to the minimum value.
(0.90 * 350) + 300 = 615 miles. So on the 10 percent of days with the highest mileage, the driver travels at least 615 miles.