Answer to Question #337979 in Statistics and Probability for sophie

Question

the waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 8 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes

Answer 1

We have a uniform distribution, a=0, b=8.

The probability that X takes on a value between x₁ and x₂ can be found by the following formula:

$P(x_1<X<x_2)=\cfrac{x_2-x_1}{b-a},\\ P(4.25<X<8)=\cfrac{8-4.25}{8-0}=0.46875.$