Answer:
12.5% probability that the truck driver goes more than 650 miles in a day
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x or equal is given by the following formula.
![P(X \leq x) = \frac{x - a}{b-a}](https://tex.z-dn.net/?f=P%28X%20%5Cleq%20x%29%20%3D%20%5Cfrac%7Bx%20-%20a%7D%7Bb-a%7D)
The number of miles driven by a truck driver falls between 300 and 700, and follows a uniform distribution.
This means that ![a = 300, b = 700](https://tex.z-dn.net/?f=a%20%3D%20300%2C%20b%20%3D%20700)
What is the probability that the truck driver goes more than 650 miles in a day?
Either he goes 650 miles or less, or he goes more than 650 miles. The sum of the probabilities of these events is 1. So
![P(X \leq 650) + P(X > 650) = 1](https://tex.z-dn.net/?f=P%28X%20%5Cleq%20650%29%20%2B%20P%28X%20%3E%20650%29%20%3D%201)
![P(X > 650) = 1 - P(X \leq 650) = 1 - \frac{650 - 300}{700 - 300} = 0.125](https://tex.z-dn.net/?f=P%28X%20%3E%20650%29%20%3D%201%20-%20P%28X%20%5Cleq%20650%29%20%3D%201%20-%20%5Cfrac%7B650%20-%20300%7D%7B700%20-%20300%7D%20%3D%200.125)
12.5% probability that the truck driver goes more than 650 miles in a day