Question

Which is the largest limit available for commercial vehicles in the residual market?

1) Any higher limits required by any law
2) 100/300/50
3) 250/500/250
4) 250/500/100

Answer 1

The probability that a truck driver drives more than 650 miles in a day is 12.5%. The probability of driving between 400 and 650 miles in a day is 62.5%. The driver will travel at least 660 miles on the days within the highest 10 percent mileage.

Step-by-step explanation:

The question asks about the probability of certain events occurring under a uniform distribution where a truck driver's miles driven in a day range from 300 to 700 miles.

1. Probability of driving more than 650 miles in a day: Since the distribution is uniform, the probability is the length of the interval where the event occurs divided by the total length of the distribution.
2. The interval for this event is from 650 to 700 miles, which is 50 miles. The total interval is 400 miles (700 - 300). Therefore, the probability P(X > 650) = 50/400 = 0.125 or 12.5%.
3. Probability of driving between 400 and 650 miles in a day: The interval for this event is 250 miles (650 - 400). Again, using the total interval of 400 miles, the probability P(400 < X < 650) = 250/400 = 0.625 or 62.5%.
4. The truck driver travels at least how many miles on the days with the highest 10 percent of mileage? The highest 10 percent tail of a uniform distribution starts at the 90th percentile.
5. To find this value, we calculate the range (400 miles) and multiply it by 0.9, then add the result to the minimum value (300 miles). 400 * 0.9 + 300 = 660 miles. So, the driver travels at least 660 miles on those days.