Question

Trucks in a delivery fleet travel a man of 120 miles per day with a santa deviation of 17 miles per day the mileage per day it’s just a beat it normally find the probability that a truck driver between 130 and 137 miles in the day round your answer to four decimal places

Answer 1

The probability of a truck driver driving more than 650 miles in a day in a uniform distribution between 300 and 700 miles is 0.125. The probability of driving between 400 and 650 miles is 0.625. On the top 10 percent of days with the highest mileage, the driver travels at least 660 miles.

Step-by-step explanation:

To compute the probability of an event in a uniform distribution, we use the formula P(a < X < b) = (b - a) / (c - d), where X is a continuous random variable, a and b define the range of interest, and c and d are the parameters of the uniform distribution which define the minimum and maximum values, respectively.

For the scenario where the number of miles driven by a truck driver follows a uniform distribution between 300 and 700 miles:

1. Probability of driving more than 650 miles: P(X > 650) = (700 - 650) / (700 - 300) = 50 / 400 = 0.125.
2. Probability of driving between 400 and 650 miles: P(400 < X < 650) = (650 - 400) / (700 - 300) = 250 / 400 = 0.625.
3. To find the mileage corresponding to the top 10 percent of days in terms of mileage, we look for the value X such that 10% of the distribution lies above X. Since the distribution is uniform, this is simply the 90th percentile, which is 0.90 * (700 - 300) + 300 = 660 miles.

These calculations help us understand probabilities and decisions involved in logistics and transportation services, ensuring efficiency and reliability in a fleet's operations.