Final answer:
A person can feasibly drive across the United States from Florida to California in 0.5 week. The probability of a truck driver driving more than 650 miles in a day is 0.125, between 400 and 650 miles is 0.625, and the mileage for the top 10 percent of highest mileage days is at least 660 miles.
Step-by-step explanation:
When answering the question about whether a person can drive across the United States from Florida to California in a week, we can utilize some mathematical concepts to calculate travel times. Since a typical driving distance for this cross-country journey might be around 2,500 to 3,000 miles, and an average driver might cover around 500 miles per day with reasonable breaks, it's quite feasible to complete the drive in less than a week. Therefore, the correct answer to the student's question is option b, 0.5 week.
For the truck driver's mileage probabilities given the information that the mileages follow a uniform distribution between 300 and 700 miles:
- The probability that the truck driver goes more than 650 miles in a day is the probability that the mileage falls in the range of (650, 700]. To calculate this, we find the length of the interval (700 - 650 = 50) and divide by the total mileage range (700 - 300 = 400). Therefore, the probability is 50/400 or an equivalent of 0.125.
- To find the probability that the truck driver goes between 400 and 650 miles in a day, we calculate the interval length (650 - 400 = 250) and again divide by the total mileage range (700 - 300 = 400), giving us a probability of 250/400 or 0.625.
- For the miles the truck driver travels on the 10 percent of days with the highest mileage, we're looking for the 90th percentile. Since it's a uniform distribution, we can simply calculate 90% of the total range added to the minimum mileage: 0.90 * (700 - 300) + 300 = 360 + 300 = 660 miles.