Question

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 7 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.

Answer 1

The probability that a randomly selected passenger has a waiting time greater than 2.25 minutes is P=0.68.

Explanation:

For a uniform distribution, any value within the minimum and maximum value have the same probability. Outside that interval, the probability is 0.

Then, for a uniform distribution within a and b, the probability P(X>c), being z<c<b is:

`P(X>c)=(b-c)/(b-a)`

For our case, with a uniform distribution within 0 and 7 minutes, the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes is:

`P(t>2.25)=(7-2.25)/(7-0)=(4.75)/(7)=0.68`