Final answer:
In mathematics, the probability for a truck driver's miles driven being more than 650 miles is 12.5%, between 400 and 650 miles is 62.5%, and at least 660 miles on the highest 10 percent of days, using uniform distribution for calculation.
Step-by-step explanation:
Determining the probability of various driving distances for a truck driver follows a mathematical approach involving uniform distribution. If the number of miles driven falls between 300 and 700 miles, uniformly distributed, the calculations for probability are based on the length of the interval of interest over the total possible interval length.
- To find the probability that the truck driver goes more than 650 miles in a day, you look at the interval from 650 to 700 miles, which is 50 miles wide. Because the entire range is 400 miles (from 300 to 700), the probability is 50/400 or 0.125 (12.5%).
- For the probability that the truck driver goes between 400 and 650 miles, this interval is 250 miles wide. Thus, the probability is 250/400 or 0.625 (62.5%).
- To determine the distance traveled on the 10 percent of days with the highest mileage, you would calculate the 90th percentile of the distribution, which in this case is 300 miles plus 90% of 400, equating to 660 miles.