Question

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.

Answer 1

Answer: 0.625

Step-by-step explanation:

Given : The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed with interval= [0 minutes, 6 minutes]

The probability density function :-

$f(x)=\dfrac{1}{6-0}=\dfrac{1}{6}$

The interval of  required event = [2.25 seconds, 6 seconds]

Now, the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes is given by :-

$\dfrac{6-2.25}{6}=\dfrac{3.75}{6}=0.625$

Hence, the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes = 0.625